Spatial noise-aware temperature retrieval from infrared sounder data

In this paper we present a combined strategy for the retrieval of atmospheric profiles from infrared sounders. The approach considers the spatial information and a noise-dependent dimensionality reduction approach. The extracted features are fed into a canonical linear regression. We compare Principal Component Analysis (PCA) and Minimum Noise Fraction (MNF) for dimensionality reduction, and study the compactness and information content of the extracted features. Assessment of the results is done on a big dataset covering many spatial and temporal situations. PCA is widely used for these purposes but our analysis shows that one can gain significant improvements of the error rates when using…

Disentangling Derivatives, Uncertainty and Error in Gaussian Process Models

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval. An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and testing points, only in the observations. However, this is often not the case in Earth observation problems where an accurate assessment of the instrument error is usually a…

Replacing radiative transfer models by surrogate approximations through machine learning

Physically-based radiative transfer models (RTMs) help in understanding the processes occurring on the Earth's surface and their interactions with vegetation and atmosphere. However, advanced RTMs can take a long computational time, which makes them unfeasible in many real applications. To overcome this problem, it has been proposed to substitute RTMs through so-called emulators. Emulators are statistical models that approximate the functioning of RTMs. They are advantageous in real practice because of the computational efficiency and excellent accuracy and flexibility for extrapolation. We here present an ‘Emulator toolbox’ that enables analyzing three multi-output machine learning regress…

Support vector machines in engineering: an overview

This paper provides an overview of the support vector machine SVM methodology and its applicability to real-world engineering problems. Specifically, the aim of this study is to review the current state of the SVM technique, and to show some of its latest successful results in real-world problems present in different engineering fields. The paper starts by reviewing the main basic concepts of SVMs and kernel methods. Kernel theory, SVMs, support vector regression SVR, and SVM in signal processing and hybridization of SVMs with meta-heuristics are fully described in the first part of this paper. The adoption of SVMs in engineering is nowadays a fact. As we illustrate in this paper, SVMs can …

Multitemporal fusion of Landsat and MERIS images

Monitoring Earth dynamics from current and future observation satellites is one of the most important objectives for the remote sensing community. In this regard, the exploitation of image time series from sensors with different characteristics provides an opportunity to increase the knowledge about environmental changes, which are needed in many operational applications, such as monitoring vegetation dynamics and land cover/use changes. Many studies in the literature have proven that high spatial resolution sensors like Landsat are very useful for monitoring land cover changes. However, the cloud cover probability of many areas and the 15-days temporal resolution restrict its use to monito…

Semi-Supervised Classification Method for Hyperspectral Remote Sensing Images

A new approach to the classification of hyperspectral images is proposed. The main problem with supervised methods is that the learning process heavily depends on the quality of the training data set. In remote sensing, the training set is useful only for simultaneous images or for images with the same classes taken under the same conditions; and, even worse, the training set is frequently not available. On the other hand, unsupervised methods are not sensitive to the number of labelled samples since they work on the whole image. Nevertheless, relationship between clusters and classes is not ensured. In this context, we propose a combined strategy of supervised and unsupervised learning met…

A support vector domain method for change detection in multitemporal images

This paper formulates the problem of distinguishing changed from unchanged pixels in multitemporal remote sensing images as a minimum enclosing ball (MEB) problem with changed pixels as target class. The definition of the sphere-shaped decision boundary with minimal volume that embraces changed pixels is approached in the context of the support vector formalism adopting a support vector domain description (SVDD) one-class classifier. SVDD maps the data into a high dimensional feature space where the spherical support of the high dimensional distribution of changed pixels is computed. Unlike the standard SVDD, the proposed formulation of the SVDD uses both target and outlier samples for defi…

Discovering single classes in remote sensing images with active learning

When dealing with supervised target detection, the acquisition of labeled samples is one of the most critical phases: the samples must be yet representative of the class of interest, but must also be found among a vast majority of non-target examples. Moreover, the efficiency of the search is also an issue, since the samples labeled as background are not used by target detectors such as the support vector data description (SVDD). In this work we propose a competitive and effective approach to identify the most relevant training samples for one-class classification based on the use of an active learning strategy. The SVDD classifier is first trained with insufficient target examples. It is t…

Kernel Anomalous Change Detection for Remote Sensing Imagery

Anomalous change detection (ACD) is an important problem in remote sensing image processing. Detecting not only pervasive but also anomalous or extreme changes has many applications for which methodologies are available. This paper introduces a nonlinear extension of a full family of anomalous change detectors. In particular, we focus on algorithms that utilize Gaussian and elliptically contoured (EC) distribution and extend them to their nonlinear counterparts based on the theory of reproducing kernels' Hilbert space. We illustrate the performance of the kernel methods introduced in both pervasive and ACD problems with real and simulated changes in multispectral and hyperspectral imagery w…

Multi-Temporal Image Classification with Kernels

Modelling spatial and spectral systematic noise patterns on CHRIS/PROBA hyperspectral data

In addition to typical random noise, remote sensing hyperspectral images are generally affected by non-periodic partially deterministic disturbance patterns due to the image formation process and characterized by a high degree of spatial and spectral coherence. This paper presents a new technique that faces the problem of removing the spatial coherent noise known as vertical stripping (VS) usually found in images acquired by push-broom sensors, in particular for the Compact High Resolution Imaging Spectrometer (CHRIS). The correction is based on the hypothesis that the vertical disturbance presents higher spatial frequencies than the surface radiance. The proposed method introduces a way to…

Physics-Aware Machine Learning For Geosciences And Remote Sensing

Machine learning models alone are excellent approximators, but very often do not respect the most elementary laws of physics, like mass or energy conservation, so consistency and confidence are compromised. In this paper we describe the main challenges ahead in the field, and introduce several ways to live in the Physics and machine learning interplay: encoding differential equations from data, constraining data-driven models with physics-priors and dependence constraints, improving parameterizations, emulating physical models, and blending data-driven and process-based models. This is a collective long-term AI agenda towards developing and applying algorithms capable of discovering knowled…

Explicit signal to noise ratio in reproducing kernel Hilbert spaces

This paper introduces a nonlinear feature extraction method based on kernels for remote sensing data analysis. The proposed approach is based on the minimum noise fraction (MNF) transform, which maximizes the signal variance while also minimizing the estimated noise variance. We here propose an alternative kernel MNF (KMNF) in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This enables KMNF dealing with non-linear relations between the noise and the signal features jointly. Results show that the proposed KMNF provides the most noise-free features when confronted with PCA, MNF, KPCA, and the previous version of KMNF. Extracted features with the explicit KMNF…

Down-Scaling Modis Vegetation Products with Landsat GAP Filled Surface Reflectance in Google Earth Engine

High spatial resolution vegetation products are fundamental in different fields, such as improving the understanding of crop seasonality at regional scales. Here, two new vegetation products such as the Leaf Area Index (LAI) and the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) are downscaled at continental scales. A novel HIghly Scalable Temporal Adaptive Reflectance Fusion Model (HIS-TARFM) is used to generate the gap-free time series of Landsat surface reflectance data by fusing MODIS and Landsat reflectance for the contiguous United States. An artificial neural network is trained to capture the relationship between the gap free Landsat surface reflectance and the MODI…

Sensitivity analysis of Gaussian processes for oceanic chlorophyll prediction

Gaussian Process Regression (GPR) for machine learning has lately been successfully introduced for chlorophyll content mapping from remotely sensed data. The method provides a fast, stable and accurate prediction of biophysical parameters. However, since GPR is a non-linear kernel regression method, the relevance of the features are not accessible. In this paper, we introduce a probabilistic approach for feature sensitivity analysis (SA) of the GPR in order to reveal the relative importance of the features (bands) being used in the regression process. We evaluated the SA on GPR ocean chlorophyll content prediction. The method revealed the importance of the spectral bands, thus allowing the …

Statistical biophysical parameter retrieval and emulation with Gaussian processes

Abstract Earth observation from satellites poses challenging problems where machine learning is being widely adopted as a key player. Perhaps the most challenging scenario that we are facing nowadays is to provide accurate estimates of particular variables of interest characterizing the Earth's surface. This chapter introduces some recent advances in statistical bio-geophysical parameter retrieval from satellite data. In particular, we will focus on Gaussian process regression (GPR) that has excelled in parameter estimation as well as in modeling complex radiative transfer processes. GPR is based on solid Bayesian statistics and generally yields efficient and accurate parameter estimates, a…

The FLUXCOM ensemble of global land-atmosphere energy fluxes

Although a key driver of Earth’s climate system, global land-atmosphere energy fluxes are poorly constrained. Here we use machine learning to merge energy flux measurements from FLUXNET eddy covariance towers with remote sensing and meteorological data to estimate global gridded net radiation, latent and sensible heat and their uncertainties. The resulting FLUXCOM database comprises 147 products in two setups: (1) 0.0833° resolution using MODIS remote sensing data (RS) and (2) 0.5° resolution using remote sensing and meteorological data (RS + METEO). Within each setup we use a full factorial design across machine learning methods, forcing datasets and energy balance closure corrections. For…

Kernel Spectral Angle Mapper

This communication introduces a very simple generalization of the familiar spectral angle mapper (SAM) distance. SAM is perhaps the most widely used distance in chemometrics, hyperspectral imaging, and remote sensing applications. We show that a nonlinear version of SAM can be readily obtained by measuring the angle between pairs of vectors in a reproducing kernel Hilbert spaces. The kernel SAM generalizes the angle measure to higher-order statistics, it is a valid reproducing kernel, it is universal, and it has consistent geometrical properties that permit deriving a metric easily. We illustrate its performance in a target detection problem using very high resolution imagery. Excellent re…

Quantifying Vegetation Biophysical Variables from Imaging Spectroscopy Data: A Review on Retrieval Methods

An unprecedented spectroscopic data stream will soon become available with forthcoming Earth-observing satellite missions equipped with imaging spectroradiometers. This data stream will open up a vast array of opportunities to quantify a diversity of biochemical and structural vegetation properties. The processing requirements for such large data streams require reliable retrieval techniques enabling the spatiotemporally explicit quantification of biophysical variables. With the aim of preparing for this new era of Earth observation, this review summarizes the state-of-the-art retrieval methods that have been applied in experimental imaging spectroscopy studies inferring all kinds of vegeta…

Measuring the Spatial and Spectral Performance of WorldView-3

The new WorldView-3 satellite provides a unique combination of very high spatial resolution and super-spectral capabilities. This presentation explores the practical and theoretical usefulness of this platform as compared against other hyperspectral and multispectral sensors.

Uncertainty analysis of gross primary production upscaling using Random Forests, remote sensing and eddy covariance data

Abstract The accurate quantification of carbon fluxes at continental spatial scale is important for future policy decisions in the context of global climate change. However, many elements contribute to the uncertainty of such estimate. In this study, the uncertainties of eight days gross primary production (GPP) predicted by Random Forest (RF) machine learning models were analysed at the site, ecosystem and European spatial scales. At the site level, the uncertainties caused by the missing of key drivers were evaluated. The most accurate predictions of eight days GPP were obtained when all available drivers were used (Pearson's correlation coefficient, ρ ~ 0.84; Root Mean Square Error (RMSE…

Constraining Uncertainty in Projected Gross Primary Production With Machine Learning

The terrestrial biosphere is currently slowing down global warming by absorbing about 30% of human emissions of carbon dioxide (CO2). The largest flux of the terrestrial carbon uptake is gross primary production (GPP) defined as the production of carbohydrates by photosynthesis. Elevated atmospheric CO2 concentration is expected to increase GPP (“CO2 fertilization effect”). However, Earth system models (ESMs) exhibit a large range in simulated GPP projections. In this study, we combine an existing emergent constraint on CO2 fertilization with a machine learning approach to constrain the spatial variations of multimodel GPP projections. In a first step, we use observed changes in the CO2 sea…

Improved Statistically Based Retrievals via Spatial-Spectral Data Compression for IASI Data

In this paper, we analyze the effect of spatial and spectral compression on the performance of statistically based retrieval. Although the quality of the information is not com- pletely preserved during the coding process, experiments reveal that a certain amount of compression may yield a positive impact on the accuracy of retrievals. We unveil two strategies, both with interesting benefits: either to apply a very high compression, which still maintains the same retrieval performance as that obtained for uncompressed data; or to apply a moderate to high compression, which improves the performance. As a second contribution of this paper, we focus on the origins of these benefits. On the one…

The Low Dimensionality of Development

AbstractThe World Bank routinely publishes over 1500 “World Development Indicators” to track the socioeconomic development at the country level. A range of indices has been proposed to interpret this information. For instance, the “Human Development Index” was designed to specifically capture development in terms of life expectancy, education, and standard of living. However, the general question which independent dimensions are essential to capture all aspects of development still remains open. Using a nonlinear dimensionality reduction approach we aim to extract the core dimensions of development in a highly efficient way. We find that more than 90% of variance in the WDIs can be represen…

Multitemporal Unmixing of Medium-Spatial-Resolution Satellite Images: A Case Study Using MERIS Images for Land-Cover Mapping

Data from current medium-spatial-resolution imaging spectroradiometers are used for land-cover mapping and land-cover change detection at regional to global scales. However, few landscapes are homogeneous at these scales, and this creates the so-called mixed-pixel problem. In this context, this study explores the use of the linear spectral mixture model to extract subpixel land-cover composition from medium-spatial-resolution data. In particular, a time series of MEdium Resolution Imaging Spectrometer (MERIS) full-resolution (FR; pixel size of 300 m) images acquired over The Netherlands is used to illustrate this study. The Netherlands was selected because of the following: 1) the fragmenta…

Nonlinear Distribution Regression for Remote Sensing Applications

In many remote sensing applications, one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms, such as neural networks, random forests, or the Gaussian processes, are readily available to relate the two. However, we often encounter situations where the target variable is only available at the group level, i.e., collectively associated with a number of remotely sensed observations. This problem setting is known in statistics and machine learning as multiple instance learning (MIL) or distribution regression (DR). This article introduces a nonlinear (kern…

Causal Inference in Geoscience and Remote Sensing From Observational Data

Establishing causal relations between random variables from observational data is perhaps the most important challenge in today’s science. In remote sensing and geosciences, this is of special relevance to better understand the earth’s system and the complex interactions between the governing processes. In this paper, we focus on an observational causal inference, and thus, we try to estimate the correct direction of causation using a finite set of empirical data. In addition, we focus on the more complex bivariate scenario that requires strong assumptions and no conditional independence tests can be used. In particular, we explore the framework of (nondeterministic) additive noise models, …

Nonlinear Cook distance for Anomalous Change Detection

In this work we propose a method to find anomalous changes in remote sensing images based on the chronochrome approach. A regressor between images is used to discover the most {\em influential points} in the observed data. Typically, the pixels with largest residuals are decided to be anomalous changes. In order to find the anomalous pixels we consider the Cook distance and propose its nonlinear extension using random Fourier features as an efficient nonlinear measure of impact. Good empirical performance is shown over different multispectral images both visually and quantitatively evaluated with ROC curves.

Physics-Aware Gaussian Processes for Earth Observation

Earth observation from satellite sensory data pose challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression and other kernel methods have excelled in biophysical parameter estimation tasks from space. GP regression is based on solid Bayesian statistics, and generally yield efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations is available though. In this work, we review three GP models that respect and learn the physics of the underlying processes …

Automatic emulator and optimized look-up table generation for radiative transfer models

This paper introduces an automatic methodology to construct emulators for costly radiative transfer models (RTMs). The proposed method is sequential and adaptive, and it is based on the notion of the acquisition function by which instead of optimizing the unknown RTM underlying function we propose to achieve accurate approximations. The Automatic Gaussian Process Emulator (AGAPE) methodology combines the interpolation capabilities of Gaussian processes (GPs) with the accurate design of an acquisition function that favors sampling in low density regions and flatness of the interpolation function. We illustrate the good capabilities of the method in toy examples and for the construction of an…

Non-linear RLS-based algorithm for pattern classification

A new non-linear recursive least squares (RLS) algorithm is presented in the context of pattern classification problems. The algorithm incorporates the non-linearity of the filter's output in the updating rules of the classical RLS algorithm. The proposed method yields lower stationary error levels when compared to the standard LMS and RLS algorithms in a classical application of pattern classification, such as the channel equalization problem.

Hyperspectral detection of citrus damage with Mahalanobis kernel classifier

Presented is a full computer vision system for the identification of post-harvest damage in citrus packing houses. The method is based on the combined use of hyperspectral images and the Mahalanobis kernel classifier. More accurate and reliable results compared to other methods are obtained in several scenarios and acquired images.

Multispectral high resolution sensor fusion for smoothing and gap-filling in the cloud

Remote sensing optical sensors onboard operational satellites cannot have high spectral, spatial and temporal resolutions simultaneously. In addition, clouds and aerosols can adversely affect the signal contaminating the land surface observations. We present a HIghly Scalable Temporal Adaptive Reflectance Fusion Model (HISTARFM) algorithm to combine multispectral images of different sensors to reduce noise and produce monthly gap free high resolution (30 m) observations over land. Our approach uses images from the Landsat (30 m spatial resolution and 16 day revisit cycle) and the MODIS missions, both from Terra and Aqua platforms (500 m spatial resolution and daily revisit cycle). We implem…

PRINCIPAL POLYNOMIAL ANALYSIS

© 2014 World Scientific Publishing Company. This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of maximal variance by means of curves instead of straight lines. Contrarily to previous approaches PPA reduces to performing simple univariate regressions which makes it computationally feasible and robust. Moreover PPA shows a number of interesting analytical properties. First PPA is a volume preserving map which in turn guarantees the existence of the inverse. Second such an inverse can be obtained…

Introduction to the Issue on Advances in Remote Sensing Image Processing

The papers in this special issue span a wide range of problems arising in modern remote sensing data analysis and provide a snapshot in the state-of-the-art of remote sensing image processing. More advances are expected in the near future, mainly due to the increasing user demands in terms of spatial, spectral, and temporal resolutions of data, and of products generated from these data by automatic processing techniques.

Semi-supervised Hyperspectral Image Classification with Graphs

This paper presents a semi-supervised graph-based method for the classification of hyperspectral images. The method is designed to exploit the spatial/contextual information in the im- ages through composite kernels. The proposed method produces smoother classifications with respect to the intrinsic structure collectively revealed by known labeled and unlabeled points. Good accuracy in high dimensional spaces and low number of labeled samples (ill-posed situations) are produced as compared to standard inductive support vector machines.

Advances in Kernel Machines for Image Classification and Biophysical Parameter Retrieval

Remote sensing data analysis is knowing an unprecedented upswing fostered by the activities of the public and private sectors of geospatial and environmental data analysis. Modern imaging sensors offer the necessary spatial and spectral information to tackle a wide range problems through Earth Observation, such as land cover and use updating, urban dynamics, or vegetation and crop monitoring. In the upcoming years even richer information will be available: more sophisticated hyperspectral sensors with high spectral resolution, multispectral sensors with sub-metric spatial detail or drones that can be deployed in very short time lapses. Besides such opportunities, these new and wealthy infor…

Structured Output SVM for Remote Sensing Image Classification

Traditional kernel classifiers assume independence among the classification outputs. As a consequence, each misclassification receives the same weight in the loss function. Moreover, the kernel function only takes into account the similarity between input values and ignores possible relationships between the classes to be predicted. These assumptions are not consistent for most of real-life problems. In the particular case of remote sensing data, this is not a good assumption either. Segmentation of images acquired by airborne or satellite sensors is a very active field of research in which one tries to classify a pixel into a predefined set of classes of interest (e.g. water, grass, trees,…

Randomized kernels for large scale Earth observation applications

Abstract Current remote sensing applications of bio-geophysical parameter estimation and image classification have to deal with an unprecedented big amount of heterogeneous and complex data sources. New satellite sensors involving a high number of improved time, space and wavelength resolutions give rise to challenging computational problems. Standard physical inversion techniques cannot cope efficiently with this new scenario. Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in the last years to develop st…

Predicting year of plantation with hyperspectral and lidar data

This paper introduces a methodology for predicting the year of plantation (YOP) from remote sensing data. The application has important implications in forestry management and inventorying. We exploit hyperspectral and LiDAR data in combination with state-of-the-art machine learning classifiers. In particular, we present a complete processing chain to extract spectral, textural and morphological features from both sensory data. Features are then combined and fed a Gaussian Process Classifier (GPC) trained to predict YOP in a forest area in North Carolina (US). The GPC algorithm provides accurate YOP estimates, reports spatially explicit maps and associated confidence maps, and provides sens…

Foetal ECG recovery using dynamic neural networks

Non-invasive electrocardiography has proven to be a very interesting method for obtaining information about the foetus state and thus to assure its well-being during pregnancy. One of the main applications in this field is foetal electrocardiogram (ECG) recovery by means of automatic methods. Evident problems found in the literature are the limited number of available registers, the lack of performance indicators, and the limited use of non-linear adaptive methods. In order to circumvent these problems, we first introduce the generation of synthetic registers and discuss the influence of different kinds of noise to the modelling. Second, a method which is based on numerical (correlation coe…

Retrieval of Physical Parameters With Deep Structured Kernel Regression

A Unified SVM Framework for Signal Estimation

This paper presents a unified framework to tackle estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The use of SVMs in estimation problems has been traditionally limited to its mere use as a black-box model. Noting such limitations in the literature, we take advantage of several properties of Mercer's kernels and functional analysis to develop a family of SVM methods for estimation in DSP. Three types of signal model equations are analyzed. First, when a specific time-signal structure is assumed to model the underlying system that generated the data, the linear signal model (so called Primal Signal Model formulation) is first stated and analyzed. T…

Understanding Climate Impacts on Vegetation with Gaussian Processes in Granger Causality

Global warming is leading to unprecedented changes in our planet, with great societal, economical and environmental implications, especially with the growing demand of biofuels and food. Assessing the impact of climate on vegetation is of pressing need. We approached the attribution problem with a novel nonlinear Granger causal (GC) methodology and used a large data archive of remote sensing satellite products, environmental and climatic variables spatio-temporally gridded over more than 30 years. We generalize kernel Granger causality by considering the variables cross-relations explicitly in Hilbert spaces, and use the covariance in Gaussian processes. The method generalizes the linear an…

PCA Gaussianization for image processing

The estimation of high-dimensional probability density functions (PDFs) is not an easy task for many image processing applications. The linear models assumed by widely used transforms are often quite restrictive to describe the PDF of natural images. In fact, additional non-linear processing is needed to overcome the limitations of the model. On the contrary, the class of techniques collectively known as projection pursuit, which solve the high-dimensional problem by sequential univariate solutions, may be applied to very general PDFs (e.g. iterative Gaussianization procedures). However, the associated computational cost has prevented their extensive use in image processing. In this work, w…

A Survey on Gaussian Processes for Earth-Observation Data Analysis: A Comprehensive Investigation

Gaussian processes (GPs) have experienced tremendous success in biogeophysical parameter retrieval in the last few years. GPs constitute a solid Bayesian framework to consistently formulate many function approximation problems. This article reviews the main theoretical GP developments in the field, considering new algorithms that respect signal and noise characteristics, extract knowledge via automatic relevance kernels to yield feature rankings automatically, and allow applicability of associated uncertainty intervals to transport GP models in space and time that can be used to uncover causal relations between variables and can encode physically meaningful prior knowledge via radiative tra…

Remote sensing image segmentation by active queries

Active learning deals with developing methods that select examples that may express data characteristics in a compact way. For remote sensing image segmentation, the selected samples are the most informative pixels in the image so that classifiers trained with reduced active datasets become faster and more robust. Strategies for intelligent sampling have been proposed with model-based heuristics aiming at the search of the most informative pixels to optimize model's performance. Unlike standard methods that concentrate on model optimization, here we propose a method inspired in the cluster assumption that holds in most of the remote sensing data. Starting from a complete hierarchical descri…

Spectral band selection for vegetation properties retrieval using Gaussian processes regression

Abstract With current and upcoming imaging spectrometers, automated band analysis techniques are needed to enable efficient identification of most informative bands to facilitate optimized processing of spectral data into estimates of biophysical variables. This paper introduces an automated spectral band analysis tool (BAT) based on Gaussian processes regression (GPR) for the spectral analysis of vegetation properties. The GPR-BAT procedure sequentially backwards removes the least contributing band in the regression model for a given variable until only one band is kept. GPR-BAT is implemented within the framework of the free ARTMO's MLRA (machine learning regression algorithms) toolbox, w…

Generation of global vegetation products from EUMETSAT AVHRR/METOP satellites

We describe the methodology applied for the retrieval of global LAI, FAPAR and FVC from Advanced Very High Resolution Radiometer (AVHRR) onboard the Meteorological-Operational (MetOp) polar orbiting satellites also known as EUMETSAT Polar System (EPS). A novel approach has been developed for the joint retrieval of three parameters (LAI, FVC, and FAPAR) instead of training one model per parameter. The method relies on multi-output Gaussian Processes Regression (GPR) trained over PROSAIL EPS simulations. A sensitivity analysis is performed to assess several sources of uncertainties in retrievals and maximize the positive impact of modeling the noise in training simulations. We describe the ma…

Estimating biophysical variable dependences with kernels

This paper introduces a nonlinear measure of dependence between random variables in the context of remote sensing data analysis. The Hilbert-Schmidt Independence Criterion (HSIC) is a kernel method for evaluating statistical dependence. HSIC is based on computing the Hilbert-Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces. The HSIC empirical estimator is very easy to compute and has good theoretical and practical properties. We exploit the capabilities of HSIC to explain nonlinear dependences in two remote sensing problems: temperature estimation and chlorophyll concentration prediction from spectra. Results show that, when the relationshi…

A kernel regression approach to cloud and shadow detection in multitemporal images

Earth observation satellites will provide in the next years time series with enough revisit time allowing a better surface monitoring. In this work, we propose a cloud screening and a cloud shadow detection method based on detecting abrupt changes in the temporal domain. It is considered that the time series follows smooth variations and abrupt changes in certain spectral features will be mainly due to the presence of clouds or cloud shadows. The method is based on linear and nonlinear regression analysis; in particular we focus on the regularized least squares and kernel regression methods. Experiments are carried out using Landsat 5 TM time series acquired over Albacete (Spain), and compa…

Global Estimation of Biophysical Variables from Google Earth Engine Platform

This paper proposes a processing chain for the derivation of global Leaf Area Index (LAI), Fraction of Absorbed Photosynthetically Active Radiation (FAPAR), Fraction Vegetation Cover (FVC), and Canopy water content (CWC) maps from 15-years of MODIS data exploiting the capabilities of the Google Earth Engine (GEE) cloud platform. The retrieval chain is based on a hybrid method inverting the PROSAIL radiative transfer model (RTM) with Random forests (RF) regression. A major feature of this work is the implementation of a retrieval chain exploiting the GEE capabilities using global and climate data records (CDR) of both MODIS surface reflectance and LAI/FAPAR datasets allowing the global estim…

Partitioning net carbon dioxide fluxes into photosynthesis and respiration using neural networks

Abstract The eddy covariance (EC) technique is used to measure the net ecosystem exchange (NEE) of CO2 between ecosystems and the atmosphere, offering a unique opportunity to study ecosystem responses to climate change. NEE is the difference between the total CO2 release due to all respiration processes (RECO), and the gross carbon uptake by photosynthesis (GPP). These two gross CO2 fluxes are derived from EC measurements by applying partitioning methods that rely on physiologically based functional relationships with a limited number of environmental drivers. However, the partitioning methods applied in the global FLUXNET network of EC observations do not account for the multiple co‐acting…

Gaussianizing the Earth: Multidimensional Information Measures for Earth Data Analysis

Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is challenging because spatio-temporal data is high-dimensional, heterogeneous and has non-linear characteristics. In this paper, we apply multivariate Gaussianization for probability density estimation which is robust to dimensionality, comes with statistical guarantees, and is easy to apply. In addition, this methodology allows us to estimate information-theoretic measures to characterize multivariate densities: information, entropy, total correlation, and mutual in…

Pattern Recognition Scheme for Large-Scale Cloud Detection over Landmarks

Landmark recognition and matching is a critical step in many Image Navigation and Registration (INR) models for geostationary satellite services, as well as to maintain the geometric quality assessment (GQA) in the instrument data processing chain of Earth observation satellites. Matching the landmark accurately is of paramount relevance, and the process can be strongly impacted by the cloud contamination of a given landmark. This paper introduces a complete pattern recognition methodology able to detect the presence of clouds over landmarks using Meteosat Second Generation (MSG) data. The methodology is based on the ensemble combination of dedicated support vector machines (SVMs) dependent…

Robust γ-filter using support vector machines

This Letter presents a new approach to time-series modelling using the support vector machines (SVM). Although the g-filter can provide stability in several time-series models, the SVM is proposed here to provide robustness in the estimation of the g-filter coefficients. Examples in chaotic time-series prediction and channel equalization show the advantages of the joint SVM g-filter. Teoría de la Señal y Comunicaciones

Living in the Physics and Machine Learning Interplay for Earth Observation

Most problems in Earth sciences aim to do inferences about the system, where accurate predictions are just a tiny part of the whole problem. Inferences mean understanding variables relations, deriving models that are physically interpretable, that are simple parsimonious, and mathematically tractable. Machine learning models alone are excellent approximators, but very often do not respect the most elementary laws of physics, like mass or energy conservation, so consistency and confidence are compromised. In this paper, we describe the main challenges ahead in the field, and introduce several ways to live in the Physics and machine learning interplay: to encode differential equations from da…

Unsupervised Anomaly and Change Detection With Multivariate Gaussianization

Anomaly detection (AD) is a field of intense research in remote sensing (RS) image processing. Identifying low probability events in RS images is a challenging problem given the high dimensionality of the data, especially when no (or little) information about the anomaly is available a priori. While a plenty of methods are available, the vast majority of them do not scale well to large datasets and require the choice of some (very often critical) hyperparameters. Therefore, unsupervised and computationally efficient detection methods become strictly necessary, especially now with the data deluge problem. In this article, we propose an unsupervised method for detecting anomalies and changes …

Inferring causal relations from observational long-term carbon and water fluxes records

AbstractLand, atmosphere and climate interact constantly and at different spatial and temporal scales. In this paper we rely on causal discovery methods to infer spatial patterns of causal relations between several key variables of the carbon and water cycles: gross primary productivity, latent heat energy flux for evaporation, surface air temperature, precipitation, soil moisture and radiation. We introduce a methodology based on the convergent cross-mapping (CCM) technique. Despite its good performance in general, CCM is sensitive to (even moderate) noise levels and hyper-parameter selection. We present a robust CCM (RCCM) that relies on temporal bootstrapping decision scores and the deri…

Systematic Assessment of MODTRAN Emulators for Atmospheric Correction

Atmospheric radiative transfer models (RTMs) simulate the light propagation in the Earth's atmosphere. With the evolution of RTMs, their increase in complexity makes them impractical in routine processing such as atmospheric correction. To overcome their computational burden, standard practice is to interpolate a multidimensional lookup table (LUT) of prestored simulations. However, accurate interpolation relies on large LUTs, which still implies large computation times for their generation and interpolation. In recent years, emulation has been proposed as an alternative to LUT interpolation. Emulation approximates the RTM outputs by a statistical regression model trained with a low number …

Kernel manifold alignment for domain adaptation

The wealth of sensory data coming from different modalities has opened numerous opportu- nities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. How- ever, multimodal architectures must rely on models able to adapt to changes in the data dis- tribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation proble…

Automatic Emulation by Adaptive Relevance Vector Machines

This paper introduces an automatic methodology to construct emulators for costly radiative transfer models (RTMs). The proposed method is sequential and adaptive, and it is based on the notion of the acquisition function by which instead of optimizing the unknown RTM underlying function we propose to achieve accurate approximations. The proposed methodology combines the interpolation capabilities of a modified Relevance Vector Machine (RVM) with the accurate design of an acquisition function that favors sampling in low density regions and flatness of the interpolation function. The proposed Relevance Vector Machine Automatic Emulator (RAE) is illustrated in toy examples and for the construc…

Ranking drivers of global carbon and energy fluxes over land

The accurate estimation of carbon and heat fluxes at global scale is paramount for future policy decisions in the context of global climate change. This paper analyzes the relative relevance of potential remote sensing and meteorological drivers of global carbon and energy fluxes over land. The study is done in an indirect way via upscaling both Gross Primary Production (GPP) and latent energy (LE) using Gaussian Process regression (GPR). In summary, GPR is successfully compared to multivariate linear regression (RMSE gain of +4.17% in GPP and +7.63% in LE) and kernel ridge regression (+2.91% in GPP and +3.07% in LE). The best GP models are then studied in terms of explanatory power based o…

Remote sensing of vegetation dynamics in agro-ecosystems using smap vegetation optical depth and optical vegetation indices

The ESA's SMOS and the NASA's SMAP missions, launched in 2009 and 2015, respectively, are the first two missions having on-board L-band microwave sensors, which are very sensitive to the water content in soils and vegetation. Focusing on the vegetation signal at L-band, we have implemented an inversion approach for SMAP that allows deriving vegetation optical depth (VOD, a microwave parameter related to biomass and plant water content) alongside soil moisture, without reliance on ancillary optical information on vegetation. This work aims at using this new observational data to monitor the phenology of crops in major global agro-ecosystems and enhance present agricultural monitoring and pre…

Statistical criteria for early-stopping of support vector machines

This paper proposes the use of statistical criteria for early-stopping support vector machines, both for regression and classification problems. The method basically stops the minimization of the primal functional when moments of the error signal (up to fourth order) become stationary, rather than according to a tolerance threshold of primal convergence itself. This simple strategy induces lower computational efforts and no significant differences are observed in terms of performance and sparsity.

A Critical Comparison of Remote Sensing Leaf Area Index Estimates over Rice-Cultivated Areas: From Sentinel-2 and Landsat-7/8 to MODIS, GEOV1 and EUMETSAT Polar System

Leaf area index (LAI) is a key biophysical variable fundamental in natural vegetation and agricultural land monitoring and modelling studies. This paper is aimed at comparing, validating and discussing different LAI satellite products from operational services and customized solution based on innovative Earth Observation (EO) data such as Landsat-7/8 and Sentinel-2A. The comparison was performed to assess overall quality of LAI estimates for rice, as a fundamental input of different scale (regional to local) operational crop monitoring systems such as the ones developed during the "An Earth obseRvation Model based RicE information Service" (ERMES) project. We adopted a multiscale approach f…

Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data

Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we pro…

From Signal Processing to Machine Learning

This chapter reviews the main landmarks of signal processing in the 20th century from the perspective of algorithmic developments. It focuses on cross‐fertilization with the field of statistical (machine) learning in the last decades. In the 21st century, model and data assumptions as well as algorithmic constraints are no longer valid, and the field of machine‐learning signal processing has erupted, with many successful stories to tell. The chapter also focuses on digital signal processing (DSP), which deals with the analysis of digitized and discrete sampled signals. Machine learning is a branch of computer science and artificial intelligence that enables computers to learn from data. Mac…

Computer Science Meets Ecology (Dagstuhl Seminar 17091)

This report summarizes the program and main outcomes of the Dagstuhl Seminar 17091 entitled ``Computer Science Meets Ecolog''. Ecology is a discipline that poses many challenging problems involving big data collection, provenance and integration, as well as difficulties in data analysis, prediction and understanding. All these issues are precisely the arena where computer science is concerned. The seminar motivation was rooted in the belief that ecology could largely benefit from modern computer science. The seminar attracted scientists from both fields who discussed important topics in ecology (e.g. botany, animal science, biogeochemistry) and how to approach them with machine learning, co…

Shared feature representations of LiDAR and optical images: Trading sparsity for semantic discrimination

This paper studies the level of complementary information conveyed by extremely high resolution LiDAR and optical images. We pursue this goal following an indirect approach via unsupervised spatial-spectral feature extraction. We used a recently presented unsupervised convolutional neural network trained to enforce both population and lifetime spar-sity in the feature representation. We derived independent and joint feature representations, and analyzed the sparsity scores and the discriminative power. Interestingly, the obtained results revealed that the RGB+LiDAR representation is no longer sparse, and the derived basis functions merge color and elevation yielding a set of more expressive…

Unsupervised change detection with kernels

In this paper an unsupervised approach to change detection relying on kernels is introduced. Kernel based clustering is used to partition a selected subset of pixels representing both changed and unchanged areas. Once the optimal clustering is obtained the estimated representatives (centroids) of each group are used to assign the class membership to all others pixels composing the multitemporal scenes. Different approaches of considering the multitemporal information are considered with accent on the computation of the difference image directly in the feature spaces. For this purpose a difference kernel approach is successfully adopted. Finally an effective way to cope with the estimation o…

Gradient-based Automatic Look-Up Table Generator for Atmospheric Radiative Transfer Models

Atmospheric correction of Earth Observation data is one of the most critical steps in the data processing chain of a satellite mission for successful remote sensing applications. Atmospheric Radiative Transfer Models (RTM) inversion methods are typically preferred due to their high accuracy. However, the execution of RTMs on a pixel-per-pixel basis is impractical due to their high computation time, thus large multi-dimensional look-up tables (LUTs) are precomputed for their later interpolation. To further reduce the RTM computation burden and the error in LUT interpolation, we have developed a method to automatically select the minimum and optimal set of nodes to be included in a LUT. We pr…

Compensatory water effects link yearly global land CO2 sink changes to temperature

Large interannual variations in the measured growth rate of atmospheric carbon dioxide (CO2) originate primarily from fluctuations in carbon uptake by land ecosystems1–3. It remains uncertain, however, to what extent temperature and water availability control the carbon balance of land ecosystems across spatial and temporal scales3–14. Here we use empirical models based on eddy covariance data15 and process-based models16,17 to investigate the effect of changes in temperature and water availability on gross primary productivity (GPP), terrestrial ecosystem respiration (TER) and net ecosystem exchange (NEE) at local and global scales. We find that water availability is the dominant driver of…

Remote Sensing Image Classification with Large Scale Gaussian Processes

Current remote sensing image classification problems have to deal with an unprecedented amount of heterogeneous and complex data sources. Upcoming missions will soon provide large data streams that will make land cover/use classification difficult. Machine learning classifiers can help at this, and many methods are currently available. A popular kernel classifier is the Gaussian process classifier (GPC), since it approaches the classification problem with a solid probabilistic treatment, thus yielding confidence intervals for the predictions as well as very competitive results to state-of-the-art neural networks and support vector machines. However, its computational cost is prohibitive for…

Foreword to the Special Issue on IGARSS 2018

The papers in this special issue were presented at the 2018 International Geoscience and Remote Sensing Symposium (IGARSS-2018) was held on July 22–27, 2018 in Valencia, Spain.

Unsupervised deep feature extraction of hyperspectral images

This paper presents an effective unsupervised sparse feature learning algorithm to train deep convolutional networks on hyperspectral images. Deep convolutional hierarchical representations are learned and then used for pixel classification. Features in lower layers present less abstract representations of data, while higher layers represent more abstract and complex characteristics. We successfully illustrate the performance of the extracted representations in a challenging AVIRIS hyperspectral image classification problem, compared to standard dimensionality reduction methods like principal component analysis (PCA) and its kernel counterpart (kPCA). The proposed method largely outperforms…

Interactive Pansharpening and Active Classification in Remote Sensing

This chapter presents two multimodal prototypes for remote sensing image classification where user interaction is an important part of the system. The first one applies pansharpening techniques to fuse a panchromatic image and a multispectral image of the same scene to obtain a high resolution (HR) multispectral image. Once the HR image has been classified the user can interact with the system to select a class of interest. The pansharpening parameters are then modified to increase the system accuracy for the selected class without deteriorating the performance of the classifier on the other classes. The second prototype utilizes Bayesian modeling and inference to implement active learning …

Nonlinear data description with Principal Polynomial Analysis

Principal Component Analysis (PCA) has been widely used for manifold description and dimensionality reduction. Performance of PCA is however hampered when data exhibits nonlinear feature relations. In this work, we propose a new framework for manifold learning based on the use of a sequence of Principal Polynomials that capture the eventually nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) is shown to generalize PCA. Unlike recently proposed nonlinear methods (e.g. spectral/kernel methods and projection pursuit techniques, neural networks), PPA features are easily interpretable and the method leads to a fully invertible transform, which is a desirable property…

A Review of Kernel Methods in ECG Signal Classification

Kernel methods have been shown to be effective in the analysis of electrocardiogram (ECG) signals. These techniques provide a consistent and well-founded theoretical framework for developing nonlinear algorithms. Kernel methods exhibit useful properties when applied to challenging design scenarios, such as: (1) when dealing with low number of (potentially high dimensional) training samples; (2) in the presence of heterogenous multimodalities; and (3) with different noise sources in the data. These characteristics are particularly appropriate for biomedical signal processing and analysis, and hence, the widespread of these techniques in biomedical signal processing in general, and in ECG dat…

Randomized Rx For Target Detection

This work tackles the target detection problem through the well-known global RX method. The RX method models the clutter as a multivariate Gaussian distribution, and has been extended to nonlinear distributions using kernel methods. While the kernel RX can cope with complex clutters, it requires a considerable amount of computational resources as the number of clutter pixels gets larger. Here we propose random Fourier features to approximate the Gaussian kernel in kernel RX and consequently our development keep the accuracy of the nonlinearity while reducing the computational cost which is now controlled by an hyperparameter. Results over both synthetic and real-world image target detection…

Recent advances in remote sensing image processing

Remote sensing image processing is nowadays a mature research area. The techniques developed in the field allow many real-life applications with great societal value. For instance, urban monitoring, fire detection or flood prediction can have a great impact on economical and environmental issues. To attain such objectives, the remote sensing community has turned into a multidisciplinary field of science that embraces physics, signal theory, computer science, electronics, and communications. From a machine learning and signal/image processing point of view, all the applications are tackled under specific formalisms, such as classification and clustering, regression and function approximation…

Retrieval of aboveground crop nitrogen content with a hybrid machine learning method

Abstract Hyperspectral acquisitions have proven to be the most informative Earth observation data source for the estimation of nitrogen (N) content, which is the main limiting nutrient for plant growth and thus agricultural production. In the past, empirical algorithms have been widely employed to retrieve information on this biochemical plant component from canopy reflectance. However, these approaches do not seek for a cause-effect relationship based on physical laws. Moreover, most studies solely relied on the correlation of chlorophyll content with nitrogen, and thus neglected the fact that most N is bound in proteins. Our study presents a hybrid retrieval method using a physically-base…

Consistent Regression of Biophysical Parameters with Kernel Methods

This paper introduces a novel statistical regression framework that allows the incorporation of consistency constraints. A linear and nonlinear (kernel-based) formulation are introduced, and both imply closed-form analytical solutions. The models exploit all the information from a set of drivers while being maximally independent of a set of auxiliary, protected variables. We successfully illustrate the performance in the estimation of chlorophyll content.

Multi-temporal and Multi-source Remote Sensing Image Classification by Nonlinear Relative Normalization

Remote sensing image classification exploiting multiple sensors is a very challenging problem: data from different modalities are affected by spectral distortions and mis-alignments of all kinds, and this hampers re-using models built for one image to be used successfully in other scenes. In order to adapt and transfer models across image acquisitions, one must be able to cope with datasets that are not co-registered, acquired under different illumination and atmospheric conditions, by different sensors, and with scarce ground references. Traditionally, methods based on histogram matching have been used. However, they fail when densities have very different shapes or when there is no corres…

Global and time-resolved monitoring of crop photosynthesis with chlorophyll fluorescence

Guanter, Luis et al.

Dosage individualization of erythropoietin using a profile-dependent support vector regression

The external administration of recombinant human erythropoietin is the chosen treatment for those patients with secondary anemia due to chronic renal failure in periodic hemodialysis. The objective of this paper is to carry out an individualized prediction of the EPO dosage to be administered to those patients. The high cost of this medication, its side-effects and the phenomenon of potential resistance which some individuals suffer all justify the need for a model which is capable of optimizing dosage individualization. A group of 110 patients and several patient factors were used to develop the models. The support vector regressor (SVR) is benchmarked with the classical multilayer percept…

Convolutional Neural Networks for Multispectral Image Cloud Masking

Convolutional neural networks (CNN) have proven to be state of the art methods for many image classification tasks and their use is rapidly increasing in remote sensing problems. One of their major strengths is that, when enough data is available, CNN perform an end-to-end learning without the need of custom feature extraction methods. In this work, we study the use of different CNN architectures for cloud masking of Proba-V multispectral images. We compare such methods with the more classical machine learning approach based on feature extraction plus supervised classification. Experimental results suggest that CNN are a promising alternative for solving cloud masking problems.

Global Estimation of Soil Moisture Persistence with L and C-Band Microwave Sensors

© 2018 IEEE Measurements of soil moisture are needed for a better global understanding of the land surface-climate feedbacks at both the local and the global scale. Satellite sensors operating in the low frequency microwave spectrum (from 1 to 10 GHz) have proven to be suitable for soil moisture retrievals. These sensors now cover nearly 4 decades thus allowing for global multi-mission climate data records. In this paper, we assess the possibility of using L-band (SMOS) and C-band (AMSR2, ASCAT) remotely sensed soil moisture time series for the global estimation of soil moisture persistence. A multi-output Gaussian process regression model is applied to ensure spatio-temporal coverage of th…

Statistical atmospheric parameter retrieval largely benefits from spatial-spectral image compression

The infrared atmospheric sounding interferometer (IASI) is flying on board of the Metop satellite series, which is part of the EUMETSAT Polar System. Products obtained from IASI data represent a significant improvement in the accuracy and quality of the measurements used for meteorological models. Notably, the IASI collects rich spectral information to derive temperature and moisture profiles, among other relevant trace gases, essential for atmospheric forecasts and for the understanding of weather. Here, we investigate the impact of near-lossless and lossy compression on IASI L1C data when statistical retrieval algorithms are later applied. We search for those compression ratios that yield…

Sparsity-Driven Digital Terrain Model Extraction

We here introduce an automatic Digital Terrain Model (DTM) extraction method. The proposed sparsity-driven DTM extractor (SD-DTM) takes a high-resolution Digital Surface Model (DSM) as an input and constructs a high-resolution DTM using the variational framework. To obtain an accurate DTM, an iterative approach is proposed for the minimization of the target variational cost function. Accuracy of the SD-DTM is shown in a real-world DSM data set. We show the efficiency and effectiveness of the approach both visually and quantitatively via residual plots in illustrative terrain types.

Fuzzy sigmoid kernel for support vector classifiers

This Letter proposes the use of the fuzzy sigmoid function presented in (IEEE Trans. Neural Networks 14(6) (2003) 1576) as non-positive semi-definite kernel in the support vector machines framework. The fuzzy sigmoid kernel allows lower computational cost, and higher rate of positive eigenvalues of the kernel matrix, which alleviates current limitations of the sigmoid kernel.

Kernel-based retrieval of atmospheric profiles from IASI data

This paper proposes the use of kernel ridge regression (KRR) to derive surface and atmospheric properties from hyperspectral infrared sounding spectra. We focus on the retrieval of temperature and humidity atmospheric profiles from Infrared Atmospheric Sounding Interferometer (MetOp-IASI) data, and provide confidence maps on the predictions. In addition, we propose a scheme for the identification of anomalies by supervised classification of discrepancies with the ECMWF estimates. For the retrieval, we observed that KRR clearly outperformed linear regression. Looking at the confidence maps, we observed that big discrepancies are mainly due to the presence of clouds and low emissivities in de…

Causal inference in geosciences with kernel sensitivity maps

Establishing causal relations between random variables from observational data is perhaps the most important challenge in today's Science. In remote sensing and geosciences this is of special relevance to better understand the Earth's system and the complex and elusive interactions between processes. In this paper we explore a framework to derive cause-effect relations from pairs of variables via regression and dependence estimation. We propose to focus on the sensitivity (curvature) of the dependence estimator to account for the asymmetry of the forward and inverse densities of approximation residuals. Results in a large collection of 28 geoscience causal inference problems demonstrate the…

Particle Group Metropolis Methods for Tracking the Leaf Area Index

Monte Carlo (MC) algorithms are widely used for Bayesian inference in statistics, signal processing, and machine learning. In this work, we introduce an Markov Chain Monte Carlo (MCMC) technique driven by a particle filter. The resulting scheme is a generalization of the so-called Particle Metropolis-Hastings (PMH) method, where a suitable Markov chain of sets of weighted samples is generated. We also introduce a marginal version for the goal of jointly inferring dynamic and static variables. The proposed algorithms outperform the corresponding standard PMH schemes, as shown by numerical experiments.

Joint Gaussian processes for inverse modeling

Solving inverse problems is central in geosciences and remote sensing. Very often a mechanistic physical model of the system exists that solves the forward problem. Inverting the implied radiative transfer model (RTM) equations numerically implies, however, challenging and computationally demanding problems. Statistical models tackle the inverse problem and predict the biophysical parameter of interest from radiance data, exploiting either in situ data or simulated data from an RTM. We introduce a novel nonlinear and nonparametric statistical inversion model which incorporates both real observations and RTM-simulated data. The proposed Joint Gaussian Process (JGP) provides a solid framework…

Retrieval of Case 2 Water Quality Parameters with Machine Learning

Water quality parameters are derived applying several machine learning regression methods on the Case2eXtreme dataset (C2X). The used data are based on Hydrolight in-water radiative transfer simulations at Sentinel-3 OLCI wavebands, and the application is done exclusively for absorbing waters with high concentrations of coloured dissolved organic matter (CDOM). The regression approaches are: regularized linear, random forest, Kernel ridge, Gaussian process and support vector regressors. The validation is made with and an independent simulation dataset. A comparison with the OLCI Neural Network Swarm (ONSS) is made as well. The best approached is applied to a sample scene and compared with t…

Information Theory in Density Destructors

Density destructors are differentiable and invertible transforms that map multivariate PDFs of arbitrary structure (low entropy) into non-structured PDFs (maximum entropy). Multivariate Gaussianization and multivariate equalization are specific examples of this family, which break down the complexity of the original PDF through a set of elementary transforms that progressively remove the structure of the data. We demonstrate how this property of density destructive flows is connected to classical information theory, and how density destructors can be used to get more accurate estimates of information theoretic quantities. Experiments with total correlation and mutual information inmultivari…

Derivation of global vegetation biophysical parameters from EUMETSAT Polar System

Abstract This paper presents the algorithm developed in LSA-SAF (Satellite Application Facility for Land Surface Analysis) for the derivation of global vegetation parameters from the AVHRR (Advanced Very High Resolution Radiometer) sensor on board MetOp (Meteorological–Operational) satellites forming the EUMETSAT (European Organization for the Exploitation of Meteorological Satellites) Polar System (EPS). The suite of LSA-SAF EPS vegetation products includes the leaf area index (LAI), the fractional vegetation cover (FVC), and the fraction of absorbed photosynthetically active radiation (FAPAR). LAI, FAPAR, and FVC characterize the structure and the functioning of vegetation and are key par…

Activities of the IEEE GRSS Spain Chapter [Chapters]

Semi-Supervised Remote Sensing Image Classification based on Clustering and the Mean Map Kernel

This paper presents a semi-supervised classifier based on the combination of the expectation-maximization (EM) algorithm for Gaussian mixture models (GMM) and the mean map kernel. The proposed method uses the most reliable samples in terms of maximum likelihood to compute a kernel function that accurately reflects the similarity between clusters in the kernel space. The proposed method improves classification accuracy in situations where the available labeled information does not properly describe the classes in the test image.

Multiset Kernel CCA for multitemporal image classification

The analysis of multitemporal remote sensing images is becoming an increasingly important problem because of the upcoming scenario of multispectral satellite constellations monitoring our Planet. Algorithms that can analyze such amount of heterogeneous information are necessary. While linear techniques have been extensively deployed, this work considers a kernel method that finds nonlinear correlations between all image sources and the class labels. We introduce in this context the Kernel Canonical Correlation Analysis (KCCA) to exploit the wealth of temporal image information and to handle nonlinear relations in a natural way via kernels. To achieve this goal, we use the generalization of …

Nonlinear Complex PCA for spatio-temporal analysis of global soil moisture

Soil moisture (SM) is a key state variable of the hydrological cycle, needed to monitor the effects of a changing climate on natural resources. Soil moisture is highly variable in space and time, presenting seasonalities, anomalies and long-term trends, but also, and important nonlinear behaviours. Here, we introduce a novel fast and nonlinear complex PCA method to analyze the spatio-temporal patterns of the Earth's surface SM. We use global SM estimates acquired during the period 2010-2017 by ESA's SMOS mission. Our approach unveils both time and space modes, trends and periodicities unlike standard PCA decompositions. Results show the distribution of the total SM variance among its differ…

Explicit Recursive and Adaptive Filtering in Reproducing Kernel Hilbert Spaces

This brief presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces. Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define the model recursivity in the Hilbert space. For that, we exploit some properties of functional analysis and recursive computation of dot products without the need of preimaging or a training dataset. We illustrate the feasibility of the methodology in the particular case of the $\gamma$ -filter, which is an infinite impulse response filter with controlled stability and memory depth. Different algorithmic formulations emerge from the signal model. Experiments in chaotic and elect…

A global Canopy Water Content product from AVHRR/Metop

Abstract Spatially and temporally explicit canopy water content (CWC) data are important for monitoring vegetation status, and constitute essential information for studying ecosystem-climate interactions. Despite many efforts there is currently no operational CWC product available to users. In the context of the Satellite Application Facility for Land Surface Analysis (LSA-SAF), we have developed an algorithm to produce a global dataset of CWC based on data from the Advanced Very High Resolution Radiometer (AVHRR) sensor on board Meteorological–Operational (MetOp) satellites forming the EUMETSAT Polar System (EPS). CWC reflects the water conditions at the leaf level and information related …

ESTIMATION OF OCEANIC PARTICULATE ORGANIC CARBON WITH MACHINE LEARNING

Understanding and quantifying ocean carbon sinks of the planet is of paramount relevance in the current scenario of global change. Particulate organic carbon (POC) is a key biogeochemical parameter that helps us characterize export processes of the ocean. Ocean color observations enable the estimation of bio-optical proxies of POC (i.e. particulate backscattering coefficient, bbp) in the surface layer of the ocean quasi-synoptically. In parallel, the Argo program distributes vertical profiles of the physical properties with a global coverage and a high spatio-temporal resolution. Merging satellite ocean color and Argo data using a neural networkbased method has already shown strong potentia…

Multitemporal and multiresolution leaf area index retrieval for operational local rice crop monitoring

Abstract This paper presents an operational chain for high-resolution leaf area index (LAI) retrieval from multiresolution satellite data specifically developed for Mediterranean rice areas. The proposed methodology is based on the inversion of the PROSAIL radiative transfer model through the state-of-the-art nonlinear Gaussian process regression (GPR) method. Landsat and SPOT5 data were used for multitemporal LAI retrievals at high-resolution. LAI estimates were validated using time series of in situ LAI measurements collected during the rice season in Spain and Italy. Ground LAI data were collected with smartphones using PocketLAI, a specific phone application for LAI estimation. Temporal…

Non-linear System Identification with Composite Relevance Vector Machines

Nonlinear system identification based on relevance vector machines (RVMs) has been traditionally addressed by stacking the input and/or output regressors and then performing standard RVM regression. This letter introduces a full family of composite kernels in order to integrate the input and output information in the mapping function efficiently and hence generalize the standard approach. An improved trade-off between accuracy and sparsity is obtained in several benchmark problems. Also, the RVM yields confidence intervals for the predictions, and it is less sensitive to free parameter selection. Teoría de la Señal y Comunicaciones

Gaussian Processes Retrieval of LAI from Sentinel-2 Top-of-Atmosphere Radiance Data

Abstract Retrieval of vegetation properties from satellite and airborne optical data usually takes place after atmospheric correction, yet it is also possible to develop retrieval algorithms directly from top-of-atmosphere (TOA) radiance data. One of the key vegetation variables that can be retrieved from at-sensor TOA radiance data is leaf area index (LAI) if algorithms account for variability in atmosphere. We demonstrate the feasibility of LAI retrieval from Sentinel-2 (S2) TOA radiance data (L1C product) in a hybrid machine learning framework. To achieve this, the coupled leaf-canopy-atmosphere radiative transfer models PROSAIL-6SV were used to simulate a look-up table (LUT) of TOA radi…

Explicit recursivity into reproducing kernel Hilbert spaces

This paper presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces (RKHS). Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define model recursivity in the Hilbert space. The method exploits some properties of functional analysis and recursive computation of dot products without the need of pre-imaging. We illustrate the feasibility of the methodology in the particular case of the gamma-filter, an infinite impulse response (IIR) filter with controlled stability and memory depth. Different algorithmic formulations emerge from the signal model. Experiments in chaotic and electroencephalographic time se…

Statistical Learning for End-to-End Simulations

End-to-end mission performance simulators (E2ES) are suitable tools to accelerate satellite mission development from concet to deployment. One core element of these E2ES is the generation of synthetic scenes that are observed by the various instruments of an Earth Observation mission. The generation of these scenes rely on Radiative Transfer Models (RTM) for the simulation of light interaction with the Earth surface and atmosphere. However, the execution of advanced RTMs is impractical due to their large computation burden. Classical interpolation and statistical emulation methods of pre-computed Look-Up Tables (LUT) are therefore common practice to generate synthetic scenes in a reasonable…

Discovering Differential Equations from Earth Observation Data

Modeling and understanding the Earth system is a constant and challenging scientific endeavour. When a clear mechanistic model is unavailable, complex or uncertain, learning from data can be an alternative. While machine learning has provided excellent methods for detection and retrieval, understanding the governing equations of the system from observational data seems an elusive problem. In this paper we introduce sparse regression to uncover a set of governing equations in the form of a system of ordinary differential equations (ODEs). The presented method is used to explicitly describe variable relations by identifying the most expressive and simplest ODEs explaining data to model releva…

Classification of Satellite Images with Regularized AdaBoosting of RBF Neural Networks

A Review of Kernel Methods in Remote Sensing Data Analysis

Kernel methods have proven effective in the analysis of images of the Earth acquired by airborne and satellite sensors. Kernel methods provide a consistent and well-founded theoretical framework for developing nonlinear techniques and have useful properties when dealing with low number of (potentially high dimensional) training samples, the presence of heterogenous multimodalities, and different noise sources in the data. These properties are particularly appropriate for remote sensing data analysis. In fact, kernel methods have improved results of parametric linear methods and neural networks in applications such as natural resource control, detection and monitoring of anthropic infrastruc…

Recycling Gibbs sampling

Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning and statistics. The key point for the successful application of the Gibbs sampler is the ability to draw samples from the full-conditional probability density functions efficiently. In the general case this is not possible, so in order to speed up the convergence of the chain, it is required to generate auxiliary samples. However, such intermediate information is finally disregarded. In this work, we show that these auxiliary samples can be recycled within the Gibbs estimators, improving their efficiency with no extra cost. Theoretical and exhaustive numerical co…

Kernel methods and their derivatives: Concept and perspectives for the earth system sciences.

Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However, kernel machines are still considered black-box models as the feature mapping is not directly accessible and difficult to interpret.The aim of this work is to show that it is indeed possible to interpret the functions learned by various kernel methods is intuitive despite their complexity. Specifically, we show that derivatives of these functions have a simple mathematical formulation, are easy to compute, and can be applied to many different problems. We n…

Explicit Granger causality in kernel Hilbert spaces

Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger causality by considering the variables cross-relations explicitly in Hilbert spaces. The framework is shown to generalize the linear and kernel GC methods, and comes with tighter bounds of performance based on Rademacher complexity. We successfully evaluate its performance in standard dynamical systems, as well as to identify the arrow of time in coupled R\"ossler systems, and is exploited to disclose the El Ni\~no-Southern Oscillation (ENSO) phenomenon f…

Understanding deep learning in land use classification based on Sentinel-2 time series

AbstractThe use of deep learning (DL) approaches for the analysis of remote sensing (RS) data is rapidly increasing. DL techniques have provided excellent results in applications ranging from parameter estimation to image classification and anomaly detection. Although the vast majority of studies report precision indicators, there is a lack of studies dealing with the interpretability of the predictions. This shortcoming hampers a wider adoption of DL approaches by a wider users community, as model’s decisions are not accountable. In applications that involve the management of public budgets or policy compliance, a better interpretability of predictions is strictly required. This work aims …

Revisiting impacts of MJO on soil moisture: a causality perspective

Cloud screening with combined MERIS and AATSR images

This paper presents a cloud screening algorithm based on ensemble methods that exploits the combined information from both MERIS and AATSR instruments on board ENVISAT in order to improve current cloud masking products for both sensors. The first step is to analyze the synergistic use of MERIS and AATSR images in order to extract some physically-based features increasing the separability of clouds and surface. Then, several artificial neural networks are trained using different sets of input features and different sets of training samples depending on acquisition and surface conditions. Finally, outputs of the trained neural networks are combined at the decision level to construct a more ac…

SCOPE-Based Emulators for Fast Generation of Synthetic Canopy Reflectance and Sun-Induced Fluorescence Spectra

Progress in advanced radiative transfer models (RTMs) led to an improved understanding of reflectance (R) and sun-induced chlorophyll fluorescence (SIF) emission throughout the leaf and canopy. Among advanced canopy RTMs that have been recently modified to deliver SIF spectral outputs are the energy balance model SCOPE and the 3D models DART and FLIGHT. The downside of these RTMs is that they are computationally expensive, which makes them impractical in routine processing, such as scene generation and retrieval applications. To bypass their computational burden, a computationally effective technique has been proposed by only using a limited number of model runs, called emulation. The idea …

Fair Kernel Learning

New social and economic activities massively exploit big data and machine learning algorithms to do inference on people’s lives. Applications include automatic curricula evaluation, wage determination, and risk assessment for credits and loans. Recently, many governments and institutions have raised concerns about the lack of fairness, equity and ethics in machine learning to treat these problems. It has been shown that not including sensitive features that bias fairness, such as gender or race, is not enough to mitigate the discrimination when other related features are included. Instead, including fairness in the objective function has been shown to be more efficient.

Learning non-linear time-scales with kernel -filters

A family of kernel methods, based on the @c-filter structure, is presented for non-linear system identification and time series prediction. The kernel trick allows us to develop the natural non-linear extension of the (linear) support vector machine (SVM) @c-filter [G. Camps-Valls, M. Martinez-Ramon, J.L. Rojo-Alvarez, E. Soria-Olivas, Robust @c-filter using support vector machines, Neurocomput. J. 62(12) (2004) 493-499.], but this approach yields a rigid system model without non-linear cross relation between time-scales. Several functional analysis properties allow us to develop a full, principled family of kernel @c-filters. The improved performance in several application examples suggest…

Cloud detection machine learning algorithms for PROBA-V

This paper presents the development and implementation of a cloud detection algorithm for Proba-V. Accurate and automatic detection of clouds in satellite scenes is a key issue for a wide range of remote sensing applications. With no accurate cloud masking, undetected clouds are one of the most significant sources of error in both sea and land cover biophysical parameter retrieval. The objective of the algorithms presented in this paper is to detect clouds accurately providing a cloud flag per pixel. For this purpose, the method exploits the information of Proba-V using statistical machine learning techniques to identify the clouds present in Proba-V products. The effectiveness of the propo…

Compressed Particle Methods for Expensive Models With Application in Astronomy and Remote Sensing

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called Approximate Bayesian Computation (ABC) sc…

Satellite Observations of the Contrasting Response of Trees and Grasses to Variations in Water Availability

Interannual variations in ecosystem primary productivity are dominated by water availability. Until recently, characterizing the photosynthetic response of different ecosystems to soil moisture anomalies was hampered by observational limitations. Here, we use a number of satellite-based proxies for productivity, including spectral indices, sun-induced chlorophyll fluorescence, and data-driven estimates of gross primary production, to reevaluate the relationship between terrestrial photosynthesis and water. In contrast to nonwoody vegetation, we find a resilience of forested ecosystems to reduced soil moisture. Sun-induced chlorophyll fluorescence and data-driven gross primary production ind…

Multitemporal fusion of Landsat/TM and ENVISAT/MERIS for crop monitoring

Abstract Monitoring Earth dynamics using current and future satellites is one of the most important objectives of the remote sensing community. The exploitation of image time series from sensors with different characteristics provides new opportunities to increase the knowledge about environmental changes and to support many operational applications. This paper presents an image fusion approach based on multiresolution and multisensor regularized spatial unmixing. The approach yields a composite image with the spatial resolution of the high spatial resolution image while retaining the spectral and temporal characteristics of the medium spatial resolution image. The approach is tested using …

Mean Kernels for Semi-Supervised Remote Sensing Image Classification

Prelaunch assessment of worldview-3 information content

The upcoming WorldView-3 satellite is designed to collect unique data by combining very-high spatial resolution (VHR) with observation bands in the short wave infrared (SWIR) in addition to the visible and near-infrared (VNIR) multispectral and panchromatic bands currently available on the VHR WorldView-2 system. These SWIR bands were specifically selected in order to target unique reflectance and absorption features presented by various surface materials and should, therefore, significantly improve the platforms information content for many image mining applications. This presentation explores the information content available to the WorldView-3 platform in two ways. First, second-order st…

Multioutput Automatic Emulator for Radiative Transfer Models

This paper introduces a methodology to construct emulators of costly radiative transfer models (RTMs). The proposed methodology is sequential and adaptive, and it is based on the notion of acquisition functions in Bayesian optimization. Here, instead of optimizing the unknown underlying RTM function, one aims to achieve accurate approximations. The Automatic Multi-Output Gaussian Process Emulator (AMO-GAPE) methodology combines the interpolation capabilities of Gaussian processes (GPs) with the accurate design of an acquisition function that favors sampling in low density regions and flatness of the interpolation function. We illustrate the promising capabilities of the method for the const…

Large scale semi-supervised image segmentation with active queries

A semiautomatic procedure to generate classification maps of remote sensing images is proposed. Starting from a hierarchical unsupervised classification, the algorithm exploits the few available labeled pixels to assign each cluster to the most probable class. For a given amount of labeled pixels, the algorithm returns a classified segmentation map, along with confidence levels of class membership for each pixel. Active learning methods are used to select the most informative samples to increase confidence in the class membership. Experiments on a AVIRIS hyperspectral image confirm the effectiveness of the method, especially when used with active learning query functions and spatial regular…

Long-term persistence, invariant time scales and on-off intermittency of fog events

Abstract In this work we study different characteristics of fog long-term persistence, in events with different physical formation mechanisms. Specifically, we focus on the characterization of fog long-term persistence from observational data, by means of a Detrended Fluctuation Analysis (DFA) of its associated low-visibility time series. We analyze fog events with radiation and orographic underlying physical formation mechanisms, and identify a two-range pattern of long-term persistence. Our analysis leads to the emergence of a characteristic time, τ∗, at the crossover point between different scaling exponents in the DFA, independent of the time scale at which the fog event is studied. We …

Learning main drivers of crop progress and failure in Europe with interpretable machine learning

Abstract A wide variety of methods exist nowadays to address the important problem of estimating crop yields from available remote sensing and climate data. Among the different approaches, machine learning (ML) techniques are being increasingly adopted, since they allow exploiting all the information on crop progress and environmental conditions and their relations with crop yield, achieving reliable and accurate estimations. However, interpreting the relationships learned by the ML models, and hence getting insights about the problem, remains a complex and usually unexplored task. Without accountability, confidence and trust in the ML models can be compromised. Here, we develop interpretab…

Dimensionality reduction via regression on hyperspectral infrared sounding data

This paper introduces a new method for dimensionality reduction via regression (DRR). The method generalizes Principal Component Analysis (PCA) in such a way that reduces the variance of the PCA scores. In order to do so, DRR relies on a deflationary process in which a non-linear regression reduces the redundancy between the PC scores. Unlike other nonlinear dimensionality reduction methods, DRR is easy to apply, it has out-of-sample extension, it is invertible, and the learned transformation is volume-preserving. These properties make the method useful for a wide range of applications, especially in very high dimensional data in general, and for hyperspectral image processing in particular…

An Emulator Toolbox to Approximate Radiative Transfer Models with Statistical Learning

Physically-based radiative transfer models (RTMs) help in understanding the processes occurring on the Earth’s surface and their interactions with vegetation and atmosphere. When it comes to studying vegetation properties, RTMs allows us to study light interception by plant canopies and are used in the retrieval of biophysical variables through model inversion. However, advanced RTMs can take a long computational time, which makes them unfeasible in many real applications. To overcome this problem, it has been proposed to substitute RTMs through so-called emulators. Emulators are statistical models that approximate the functioning of RTMs. Emulators are advantageous in real practice because…

Multitemporal unmixing of MERIS FR data

Signal-to-noise ratio in reproducing kernel Hilbert spaces

This paper introduces the kernel signal-to-noise ratio (kSNR) for different machine learning and signal processing applications}. The kSNR seeks to maximize the signal variance while minimizing the estimated noise variance explicitly in a reproducing kernel Hilbert space (rkHs). The kSNR gives rise to considering complex signal-to-noise relations beyond additive noise models, and can be seen as a useful signal-to-noise regularizer for feature extraction and dimensionality reduction. We show that the kSNR generalizes kernel PCA (and other spectral dimensionality reduction methods), least squares SVM, and kernel ridge regression to deal with cases where signal and noise cannot be assumed inde…

Principal polynomial analysis for remote sensing data processing

Inspired by the concept of Principal Curves, in this paper, we define Principal Polynomials as a non-linear generalization of Principal Components to overcome the conditional mean independence restriction of PCA. Principal Polynomials deform the straight Principal Components by minimizing the regression error (or variance) in the corresponding orthogonal subspaces. We propose to use a projection on a series of these polynomials to set a new nonlinear data representation: the Principal Polynomial Analysis (PPA). We prove that the dimensionality reduction error in PPA is always lower than in PCA. Lower truncation error and increased independence suggest that unsupervised PPA features can be b…

Interpretability of Recurrent Neural Networks in Remote Sensing

In this work we propose the use of Long Short-Term Memory (LSTM) Recurrent Neural Networks for multivariate time series of satellite data for crop yield estimation. Recurrent nets allow exploiting the temporal dimension efficiently, but interpretability is hampered by the typically overparameterized models. The focus of the study is to understand LSTM models by looking at the hidden units distribution, the impact of increasing network complexity, and the relative importance of the input covariates. We extracted time series of three variables describing the soil-vegetation status in agroe-cosystems -soil moisture, VOD and EVI- from optical and microwave satellites, as well as available in si…

Learning with the kernel signal to noise ratio

This paper presents the application of the kernel signal to noise ratio (KSNR) in the context of feature extraction to general machine learning and signal processing domains. The proposed approach maximizes the signal variance while minimizes the estimated noise variance in a reproducing kernel Hilbert space (RKHS). The KSNR can be used in any kernel method to deal with correlated (possibly non-Gaussian) noise. We illustrate the method in nonlinear regression examples, dependence estimation and causal inference, nonlinear channel equalization, and nonlinear feature extraction from high-dimensional satellite images. Results show that the proposed KSNR yields more fitted solutions and extract…

A Special Issue on Advances in Machine Learning for Remote Sensing and Geosciences [From the Guest Editors]

Machine learning has become a standard paradigm for the analysis of remote sensing and geoscience data at both local and global scales. In the upcoming years, with the advent of new satellite constellations, machine learning will have a fundamental role in processing large and heterogeneous data sources. Machine learning will move from mere statistical data processing to actual learning, understanding, and knowledge extraction. The ambitious goal is to provide responses to the challenging scientific questions about the earth system. This special issue aims at providing an updated, refreshing view of current developments in the field. For this special issue, we have collected five articles t…

Segmentation of Hyperspectral Images for the Detection of Rotten Mandarins

The detection of rotten citrus in packing lines is carried out manually under ultraviolet illumination, which is dangerous for workers. Light emitted by the rotten region of the fruit due to the ultraviolet-induced fluorescence is used by the operator to detect the damages. This procedure is required because the low contrast between the damaged and sound skin under visible illumination difficult their detection. We study a set of techniques aimed to detect rottenness in citrususing visible and near infrared lighting trough an hyperspectral imaging system. Methods for selecting a proper set of wavelengths are investigated such as correlation analysis, mutual information, stepwise or genetic …

Mapping Leaf Area Index with a Smartphone and Gaussian Processes

Leaf area index (LAI) is a key biophysical parameter used to determine foliage cover and crop growth in environmental studies. Smartphones are nowadays ubiquitous sensor devices with high computational power, moderate cost, and high-quality sensors. A smartphone app, which is called PocketLAI, was recently presented and tested for acquiring ground LAI estimates. In this letter, we explore the use of state-of-the-art nonlinear Gaussian process regression (GPR) to derive spatially explicit LAI estimates over rice using ground data from PocketLAI and Landsat 8 imagery. GPR has gained popularity in recent years because of its solid Bayesian foundations that offer not only high accuracy but also…

Lossless coding of hyperspectral images with principal polynomial analysis

The transform in image coding aims to remove redundancy among data coefficients so that they can be independently coded, and to capture most of the image information in few coefficients. While the second goal ensures that discarding coefficients will not lead to large errors, the first goal ensures that simple (point-wise) coding schemes can be applied to the retained coefficients with optimal results. Principal Component Analysis (PCA) provides the best independence and data compaction for Gaussian sources. Yet, non-linear generalizations of PCA may provide better performance for more realistic non-Gaussian sources. Principal Polynomial Analysis (PPA) generalizes PCA by removing the non-li…

Global Upscaling of the MODIS Land Cover with Google Earth Engine and Landsat Data

Image classification has become one of the most common applications in remote sensing yielding to the creation of a variety of operational thematic maps at multiple spatio-temporal scales. The information contained in these maps summarizes key characteristics related with the physical environment and provides fundamental information of the Earth for vegetation monitoring or land use status over time. However, high spatial resolution land cover maps are usually only produced for specific small regions or in an image tile. We present a general methodology to obtain a high spatial resolution land cover maps using Landsat spectral information, the powerful Google Earth Engine platform, and oper…

Spectro-temporal reflectance surfaces: a new conceptual framework for the integration of remote-sensing data from multiple different sensors

The conflict between spatial and temporal resolution of satellite systems, as well as the frequent presence of clouds in the images, has been a traditional limitation of remote sensing in the optical domain. Nevertheless, most of the conceptual tools and algorithms developed classically in remote sensing are based on the input of a series of cloud-free images from identical sensors. In this study, we propose a conceptual framework that is able to ingest data from several different sensors, make them homogeneous, eliminate clouds virtually, and make them usable in a flexible, efficient, and transparent way. The methodology is based on previous developments such as spatial ‘downscaling’, temp…

Manifold Learning with High Dimensional Model Representations

Manifold learning methods are very efficient methods for hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high input dimensional space and the (typically low) latent space is linear. This is a particularly strong assumption, especially when dealing with hyperspectral images due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on High Dimensional Model Representation (HDMR) is proposed, which enables to present a nonlinear embedding function to p…

A Support Vector Machine Signal Estimation Framework

Support vector machine (SVM) were originally conceived as efficient methods for pattern recognition and classification, and the SVR was subsequently proposed as the SVM implementation for regression and function approximation. Nowadays, the SVR and other kernel‐based regression methods have become a mature and recognized tool in digital signal processing (DSP). This chapter starts to pave the way to treat all the problems within the field of kernel machines, and presents the fundamentals for a simple, framework for tackling estimation problems in DSP using support vector machine SVM. It outlines the particular models and approximations defined within the framework. The chapter concludes wit…

Learning spatial filters for multispectral image segmentation.

International audience; We present a novel filtering method for multispectral satel- lite image classification. The proposed method learns a set of spatial filters that maximize class separability of binary support vector machine (SVM) through a gradient descent approach. Regularization issues are discussed in detail and a Frobenius-norm regularization is proposed to efficiently exclude uninformative filters coefficients. Experiments car- ried out on multiclass one-against-all classification and tar- get detection show the capabilities of the learned spatial fil- ters.

Synergistic integration of optical and microwave satellite data for crop yield estimation

Developing accurate models of crop stress, phenology and productivity is of paramount importance, given the increasing need of food. Earth observation (EO) remote sensing data provides a unique source of information to monitor crops in a temporally resolved and spatially explicit way. In this study, we propose the combination of multisensor (optical and microwave) remote sensing data for crop yield estimation and forecasting using two novel approaches. We first propose the lag between Enhanced Vegetation Index (EVI) derived from MODIS and Vegetation Optical Depth (VOD) derived from SMAP as a new joint metric combining the information from the two satellite sensors in a unique feature or des…

Spectral clustering with the probabilistic cluster kernel

Abstract This letter introduces a probabilistic cluster kernel for data clustering. The proposed kernel is computed with the composition of dot products between the posterior probabilities obtained via GMM clustering. The kernel is directly learned from the data, is parameter-free, and captures the data manifold structure at different scales. The projections in the kernel space induced by this kernel are useful for general feature extraction purposes and are here exploited in spectral clustering with the canonical k-means. The kernel structure, informative content and optimality are studied. Analysis and performance are illustrated in several real datasets.

This paper presents the use of Support Vector Machines (SVMs) for prediction and analysis of antisense oligonucleotide (AO) efficacy. The collected database comprises 315 AO molecules including 68 features each, inducing a problem well-suited to SVMs. The task of feature selection is crucial given the presence of noisy or redundant features, and the well-known problem of the curse of dimensionality. We propose a two-stage strategy to develop an optimal model: (1) feature selection using correlation analysis, mutual information, and SVM-based recursive feature elimination (SVM-RFE), and (2) AO prediction using standard and profiled SVM formulations. A profiled SVM gives different weights to …

Gradient-Based Automatic Lookup Table Generator for Radiative Transfer Models

Physically based radiative transfer models (RTMs) are widely used in Earth observation to understand the radiation processes occurring on the Earth’s surface and their interactions with water, vegetation, and atmosphere. Through continuous improvements, RTMs have increased in accuracy and representativity of complex scenes at expenses of an increase in complexity and computation time, making them impractical in various remote sensing applications. To overcome this limitation, the common practice is to precompute large lookup tables (LUTs) for their later interpolation. To further reduce the RTM computation burden and the error in LUT interpolation, we have developed a method to automaticall…

Active emulation of computer codes with Gaussian processes – Application to remote sensing

Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and exhaustive simulations. Very often such codes incorporate heuristics that ironically make them less tractable and transparent. This paper introduces an active learning methodology for adaptively constructing surrogate models, i.e. emulators, of such costly computer codes in a multi-output setting. The proposed technique is sequential and adaptive, and is based on the optimization of a suitable acquisition function. It aims to achieve accurate approximations…

Learning the relevant image features with multiple kernels

This paper proposes to learn the relevant features of remote sensing images for automatic spatio-spectral classification with the automatic optimization of multiple kernels. The method consists of building dedicated kernels for different sets of bands, contextual or textural features. The optimal linear combination of kernels is optimized through gradient descent on the support vector machine (SVM) objective function. Since a na¨ive implementation is computationally demanding, we propose an efficient model selection procedure based on kernel alignment. The result is a weight — learned from the data — for each kernel where both relevant and meaningless image features emerge after training. E…

Gridding artifacts on medium-resolution satellite image time series: MERIS case study

Earth observation satellites provide a valuable source of data which when conveniently processed can be used to better understand the Earth system dynamics. In this regard, one of the prerequisites for the analysis of satellite image time series is that the images are spatially coregistered so that the resulting multitemporal pixel entities offer a true temporal view of the area under study. This implies that all the observations must be mapped to a common system of grid cells. This process is known as gridding and, in practice, two common grids can be used as a reference: 1) a grid defined by some kind of external data set (e.g., an existing land-cover map) or 2) a grid defined by one of t…

Spectral alignment of multi-temporal cross-sensor images with automated kernel canonical correlation analysis

In this paper we present an approach to perform relative spectral alignment between optical cross-sensor acquisitions. The proposed method aims at projecting the images from two different and possibly disjoint input spaces into a common latent space, in which standard change detection algorithms can be applied. The system relies on the regularized kernel canonical correlation analysis transformation (kCCA), which can accommodate nonlinear dependencies between pixels by means of kernel functions. To learn the projections, the method employs a subset of samples belonging to the unchanged areas or to uninteresting radiometric differences. Since the availability of ground truth information to p…

Toward a Collective Agenda on AI for Earth Science Data Analysis

In the last years we have witnessed the fields of geosciences and remote sensing and artificial intelligence to become closer. Thanks to both the massive availability of observational data, improved simulations, and algorithmic advances, these disciplines have found common objectives and challenges to advance the modeling and understanding of the Earth system. Despite such great opportunities, we also observed a worrying tendency to remain in disciplinary comfort zones applying recent advances from artificial intelligence on well resolved remote sensing problems. Here we take a position on research directions where we think the interface between these fields will have the most impact and be…

Semisupervised kernel orthonormalized partial least squares

This paper presents a semisupervised kernel orthonormalized partial least squares (SS-KOPLS) algorithm for non-linear feature extraction. The proposed method finds projections that minimize the least squares regression error in Hilbert spaces and incorporates the wealth of unlabeled information to deal with small size labeled datasets. The method relies on combining a standard RBF kernel using labeled information, and a generative kernel learned by clustering all available data. The positive definiteness of the kernels is proven, and the structure and information content of the derived kernels is studied. The effectiveness of the proposed method is successfully illustrated in standard UCI d…

A family of kernel anomaly change detectors

This paper introduces the nonlinear extension of the anomaly change detection algorithms in [1] based on the theory of reproducing kernels. The presented methods generalize their linear counterparts, under both the Gaussian and elliptically-contoured assumptions, and produce both improved detection accuracies and reduced false alarm rates. We study the Gaussianity of the data in Hilbert spaces with kernel dependence estimates, provide low-rank kernel versions to cope with the high computational cost of the methods, and give prescriptions about the selection of the kernel functions and their parameters. We illustrate the performance of the introduced kernel methods in both pervasive and anom…

Deep Gaussian processes for biogeophysical parameter retrieval and model inversion

Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel based methods, and Gaussian Processes (GPs) in particular, have provided useful and informative so…

Introduction to Digital Signal Processing

Signal processing deals with the representation, transformation, and manipulation of signals and the information they contain. Typical examples include extracting the pure signals from a mixture observation (a field commonly known as deconvolution) or particular signal (frequency) components from noisy observations (generally known as filtering). This chapter outlines the basics of signal processing and then introduces the more advanced concepts of time‐frequency and time‐scale representations, as well as emerging fields of compressed sensing and multidimensional signal processing. When moving to multidimensional signal processing, a modern approach is taken from the point of view of statis…

Active Learning Methods for Efficient Hybrid Biophysical Variable Retrieval

Kernel-based machine learning regression algorithms (MLRAs) are potentially powerful methods for being implemented into operational biophysical variable retrieval schemes. However, they face difficulties in coping with large training data sets. With the increasing amount of optical remote sensing data made available for analysis and the possibility of using a large amount of simulated data from radiative transfer models (RTMs) to train kernel MLRAs, efficient data reduction techniques will need to be implemented. Active learning (AL) methods enable to select the most informative samples in a data set. This letter introduces six AL methods for achieving optimized biophysical variable estimat…

Learning drivers of climate-induced human migrations with Gaussian processes

In the current context of climate change, extreme heatwaves, droughts, and floods are not only impacting the biosphere and atmosphere but the anthroposphere too. Human populations are forcibly displaced, which are now referred to as climate-induced migrants. In this work, we investigate which climate and structural factors forced major human displacements in the presence of floods and storms during the years 2017-2019. We built, curated, and harmonized a database of meteorological and remote sensing indicators along with structural factors of 27 developing countries worldwide. We show how we can use Gaussian Processes to learn what variables can explain the impact of floods and storms in th…

Advancing Deep Learning for Earth Sciences: From Hybrid Modeling to Interpretability

Machine learning and deep learning in particular have made a huge impact in many fields of science and engineering. In the last decade, advanced deep learning methods have been developed and applied to remote sensing and geoscientific data problems extensively. Applications on classification and parameter retrieval are making a difference: methods are very accurate, can handle large amounts of data, and can deal with spatial and temporal data structures efficiently. Nevertheless, several important challenges need still to be addressed. First, current standard deep architectures cannot deal with long-range dependencies so distant driving processes (in space or time) are not captured, and the…

Deep learning and process understanding for data-driven Earth system science

Machine learning approaches are increasingly used to extract patterns and insights from the ever-increasing stream of geospatial data, but current approaches may not be optimal when system behaviour is dominated by spatial or temporal context. Here, rather than amending classical machine learning, we argue that these contextual cues should be used as part of deep learning (an approach that is able to extract spatio-temporal features automatically) to gain further process understanding of Earth system science problems, improving the predictive ability of seasonal forecasting and modelling of long-range spatial connections across multiple timescales, for example. The next step will be a hybri…

The Recycling Gibbs sampler for efficient learning

Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the successful application of the Gibbs sampler is the ability to draw efficiently samples from the full-conditional probability density functions. Since in the general case this is not possible, in order to speed up the convergence of the chain, it is required to generate auxiliary samples whose information is eventually disregarded. In this work, we show that these auxiliary sample…

Feature extraction from remote sensing data using Kernel Orthonormalized PLS

This paper presents the study of a sparse kernel-based method for non-linear feature extraction in the context of remote sensing classification and regression problems. The so-called kernel orthonormalized PLS algorithm with reduced complexity (rKOPLS) has two core parts: (i) a kernel version of OPLS (called KOPLS), and (ii) a sparse (reduced) approximation for large scale data sets, which ultimately leads to rKOPLS. The method demonstrates good capabilities in terms of expressive power of the extracted features and scalability.

Graph Embedding via High Dimensional Model Representation for Hyperspectral Images

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance to deal with hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the (typically low) latent space is linear. This is a particularly strong assump…

Support Vector Machines Framework for Linear Signal Processing

This paper presents a support vector machines (SVM) framework to deal with linear signal processing (LSP) problems. The approach relies on three basic steps for model building: (1) identifying the suitable base of the Hilbert signal space in the model, (2) using a robust cost function, and (3) minimizing a constrained, regularized functional by means of the method of Lagrange multipliers. Recently, autoregressive moving average (ARMA) system identification and non-parametric spectral analysis have been formulated under this framework. The generalized, yet simple, formulation of SVM LSP problems is particularized here for three different issues: parametric spectral estimation, stability of I…

Support Vector Machine and Kernel Classification Algorithms

This chapter introduces the basics of support vector machine (SVM) and other kernel classifiers for pattern recognition and detection. It also introduces the main elements and concept underlying the successful binary SVM. The chapter starts by introducing the main elements and concept underlying the successful binary SVM. Next, it introduces more advanced topics in SVM for classification, including large margin filtering (LMF), SSL, active learning, and large‐scale classification using SVMs. The LMF method performs both signal filtering and classification simultaneously by learning the most appropriate filters. SSL with SVMs exploits the information contained in both labeled and unlabeled e…

Cluster-based active learning for compact image classification

In this paper, we consider active sampling to label pixels grouped with hierarchical clustering. The objective of the method is to match the data relationships discovered by the clustering algorithm with the user's desired class semantics. The first is represented as a complete tree to be pruned and the second is iteratively provided by the user. The active learning algorithm proposed searches the pruning of the tree that best matches the labels of the sampled points. By choosing the part of the tree to sample from according to current pruning's uncertainty, sampling is focused on most uncertain clusters. This way, large clusters for which the class membership is already fixed are no longer…

Deep Gaussian Processes for Geophysical Parameter Retrieval

This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well to large datasets, and improves prediction accuracy over standard full and sparse GP models. We give empirical evidence of performance for estimation of surface dew point temperature from infrared sounding data.

Estimating crop primary productivity with Sentinel-2 and Landsat 8 using machine learning methods trained with radiative transfer simulations

Abstract Satellite remote sensing has been widely used in the last decades for agricultural applications, both for assessing vegetation condition and for subsequent yield prediction. Existing remote sensing-based methods to estimate gross primary productivity (GPP), which is an important variable to indicate crop photosynthetic function and stress, typically rely on empirical or semi-empirical approaches, which tend to over-simplify photosynthetic mechanisms. In this work, we take advantage of all parallel developments in mechanistic photosynthesis modeling and satellite data availability for an advanced monitoring of crop productivity. In particular, we combine process-based modeling with …

Nonlinear Time-Series Adaptation for Land Cover Classification

Automatic land cover classification from satellite image time series is of paramount relevance to assess vegetation and crop status, with important implications in agriculture, biofuels, and food. However, due to the high cost and human resources needed to characterize and classify land cover through field campaigns, a recurrent limiting factor is the lack of available labeled data. On top of this, the biophysical–geophysical variables exhibit particular temporal structures that need to be exploited. Land cover classification based on image time series is very complex because of the data manifold distortions through time. We propose the use of the kernel manifold alignment (KEMA) method for…

Gaussian processes uncertainty estimates in experimental Sentinel-2 LAI and leaf chlorophyll content retrieval

Abstract ESA’s upcoming Sentinel-2 (S2) Multispectral Instrument (MSI) foresees to provide continuity to land monitoring services by relying on optical payload with visible, near infrared and shortwave infrared sensors with high spectral, spatial and temporal resolution. This unprecedented data availability leads to an urgent need for developing robust and accurate retrieval methods, which ideally should provide uncertainty intervals for the predictions. Statistical learning regression algorithms are powerful candidats for the estimation of biophysical parameters from satellite reflectance measurements because of their ability to perform adaptive, nonlinear data fitting. In this paper, we f…

Physics-aware Gaussian processes in remote sensing

Abstract Earth observation from satellite sensory data poses challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression has excelled in biophysical parameter estimation tasks from airborne and satellite observations. GP regression is based on solid Bayesian statistics, and generally yields efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations between the state vector and the radiance observations is available though and could be useful to improve pre…

Information Theory Measures via Multidimensional Gaussianization

Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle heterogeneous data types, and the measures can be interpreted in physical units. However, it has not been adopted by a wider audience because obtaining information from multidimensional data is a challenging problem due to the curse of dimensionality. Here we propose an indirect way of computing information based on a multivariate Gaussianization transform. Our proposal mitigates the difficulty of multivariate density estimation by reducing it to a composi…

Crop Yield Estimation and Interpretability With Gaussian Processes

This work introduces the use of Gaussian processes (GPs) for the estimation and understanding of crop development and yield using multisensor satellite observations and meteo- rological data. The proposed methodology combines synergistic information on canopy greenness, biomass, soil, and plant water content from optical and microwave sensors with the atmospheric variables typically measured at meteorological stations. A com- posite covariance is used in the GP model to account for varying scales, nonstationary, and nonlinear processes. The GP model reports noticeable gains in terms of accuracy with respect to other machine learning approaches for the estimation of corn, wheat, and soybean …

Accounting for Input Noise in Gaussian Process Parameter Retrieval

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple, flexible, and provide accurate estimates. GPs are based on a Bayesian statistical framework which provides a posterior probability function for each estimation. Therefore, besides the usual prediction (given in this case by the mean function), GPs come equipped with the possibility to obtain a predictive variance (i.e., error bars, confidence intervals) for each prediction. Unfortunately, the GP formulation usually assumes that there is no noise in the inpu…

Efficient Nonlinear RX Anomaly Detectors

Current anomaly detection algorithms are typically challenged by either accuracy or efficiency. More accurate nonlinear detectors are typically slow and not scalable. In this letter, we propose two families of techniques to improve the efficiency of the standard kernel Reed-Xiaoli (RX) method for anomaly detection by approximating the kernel function with either {\em data-independent} random Fourier features or {\em data-dependent} basis with the Nystr\"om approach. We compare all methods for both real multi- and hyperspectral images. We show that the proposed efficient methods have a lower computational cost and they perform similar (or outperform) the standard kernel RX algorithm thanks t…

Hyperspectral dimensionality reduction for biophysical variable statistical retrieval

Abstract Current and upcoming airborne and spaceborne imaging spectrometers lead to vast hyperspectral data streams. This scenario calls for automated and optimized spectral dimensionality reduction techniques to enable fast and efficient hyperspectral data processing, such as inferring vegetation properties. In preparation of next generation biophysical variable retrieval methods applicable to hyperspectral data, we present the evaluation of 11 dimensionality reduction (DR) methods in combination with advanced machine learning regression algorithms (MLRAs) for statistical variable retrieval. Two unique hyperspectral datasets were analyzed on the predictive power of DR + MLRA methods to ret…

Feature selection using support vector machines and bootstrap methods for ventricular fibrillation detection

Early detection of ventricular fibrillation (VF) is crucial for the success of the defibrillation therapy in automatic devices. A high number of detectors have been proposed based on temporal, spectral, and time-frequency parameters extracted from the surface electrocardiogram (ECG), showing always a limited performance. The combination ECG parameters on different domain (time, frequency, and time-frequency) using machine learning algorithms has been used to improve detection efficiency. However, the potential utilization of a wide number of parameters benefiting machine learning schemes has raised the need of efficient feature selection (FS) procedures. In this study, we propose a novel FS…

Kernels for Remote Sensing Image Classification

Classification of images acquired by airborne and satellite sensors is a very challenging problem. These remotely sensed images usually acquire information from the scene at different wavelengths or spectral channels. The main problems involved are related to the high dimensionality of the data to be classified and the very few existing labeled samples, the diverse noise sources involved in the acquisition process, the intrinsic nonlinearity and non-Gaussianity of the data distribution in feature spaces, and the high computational cost involved to process big data cubes in near real time. The framework of statistical learning in general, and of kernel methods in particular, has gained popul…

Adaptive Kernel Learning for Signal Processing

Adaptive filtering is a central topic in digital signal processing (DSP). By applying linear adaptive filtering principles in the kernel feature space, powerful nonlinear adaptive filtering algorithms can be obtained. This chapter introduces the wide topic of adaptive signal processing, and explores the emerging field of kernel adaptive filtering (KAF). In many signal processing applications, the problem of signal estimation is addressed. Probabilistic models have proven to be very useful in this context. The chapter discusses two families of kernel adaptive filters, namely kernel least mean squares (KLMS) and kernel recursive least‐squares (KRLS) algorithms. In order to design a practical …

Recent Advances in Techniques for Hyperspectral Image Processing

International audience; Imaging spectroscopy, also known as hyperspectral imaging, has been transformed in less than thirty years from being a sparse research tool into a commodity product available to a broad user community. Currently, there is a need for standardized data processing techniques able to take into account the special properties of hyperspec- tral data. In this paper, we provide a seminal view on recent advances in techniques for hyperspectral image processing. Our main focus is on the design of techniques able to deal with the high-dimensional nature of the data, and to integrate the spa- tial and spectral information. Performance of the discussed techniques is evaluated in …

Integrating Domain Knowledge in Data-Driven Earth Observation With Process Convolutions

The modelling of Earth observation data is a challenging problem, typically approached by either purely mechanistic or purely data-driven methods. Mechanistic models encode the domain knowledge and physical rules governing the system. Such models, however, need the correct specification of all interactions between variables in the problem and the appropriate parameterization is a challenge in itself. On the other hand, machine learning approaches are flexible data-driven tools, able to approximate arbitrarily complex functions, but lack interpretability and struggle when data is scarce or in extrapolation regimes. In this paper, we argue that hybrid learning schemes that combine both approa…

Cloud-screening algorithm for ENVISAT/MERIS multispectral images

This paper presents a methodology for cloud screening of multispectral images acquired with the Medium Resolution Imaging Spectrometer (MERIS) instrument on-board the Environmental Satellite (ENVISAT). The method yields both a discrete cloud mask and a cloud-abundance product from MERIS level-lb data on a per-pixel basis. The cloud-screening method relies on the extraction of meaningful physical features (e.g., brightness and whiteness), which are combined with atmospheric-absorption features at specific MERIS-band locations (oxygen and watervapor absorptions) to increase the cloud-detection accuracy. All these features are inputs to an unsupervised classification algorithm; the cloud-proba…

Emulation as an Accurate Alternative to Interpolation in Sampling Radiative Transfer Codes

Computationally expensive radiative transfer models (RTMs) are widely used to realistically reproduce the light interaction with the earth surface and atmosphere. Because these models take long processing time, the common practice is to first generate a sparse look-up table (LUT) and then make use of interpolation methods to sample the multidimensional LUT input variable space. However, the question arise whether common interpolation methodsperform most accurate. As an alternative to interpolation, this paper proposes to use emulation, i.e., approximating the RTM output by means of the statistical learning. Two experiments were conducted to assess the accuracy in delivering spectral outputs…

Adaptive Sequential Interpolator Using Active Learning for Efficient Emulation of Complex Systems

Many fields of science and engineering require the use of complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, due to the high cost involved, the required study becomes a cumbersome process. This paper introduces an interpolation procedure which belongs to the family of active learning algorithms, in order to construct cheap surrogate models of such costly complex systems. The proposed technique is sequential and adaptive, and is based on the optimization of a suitable acquisition function. We illustrate its efficiency in a toy example and for the construction of an emulator of an atmosphere modeling system.

Assessing the relationship between microwave vegetation optical depth and gross primary production

At the global scale, the uptake of atmospheric carbon dioxide by terrestrial ecosystems through photosynthesis is commonly estimated through vegetation indices or biophysical properties derived from optical remote sensing data. Microwave observations of vegetated areas are sensitive to different components of the vegetation layer than observations in the optical domain and may therefore provide complementary information on the vegetation state, which may be used in the estimation of Gross Primary Production (GPP). However, the relation between GPP and Vegetation Optical Depth (VOD), a biophysical quantity derived from microwave observations, is not yet known. This study aims to explore the …

Spatial homogeneity from temporal stability: Exploiting the combined hyper-frequent revisit of Terra and Aqua to guide Earth System Science

Abstract The terrestrial component of the Earth system has witnessed considerable changes in the past decades due to anthropogenic action. Throughout this period, the NASA Terra mission has been constantly monitoring the surface with the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. When combined with the MODIS instrument on-board of the Aqua platform, we obtain a hyper-frequent revisit capability providing sub-daily observations globally at a moderate resolution of ~250 m, but with a strong multi-angular variation of the observation footprint. Here we propose to exploit this particular configuration provided by the combined Terra + Aqua constellation to infer spatial ho…

Optical remote sensing and the retrieval of terrestrial vegetation bio-geophysical properties – A review

Abstract: Forthcoming superspectral satellite missions dedicated to land monitoring, as well as planned imaging spectrometers, will unleash an unprecedented data stream. The processing requirements for such large data streams involve processing techniques enabling the spatio-temporally explicit quantification of vegetation properties. Typically retrieval must be accurate, robust and fast. Hence, there is a strict requirement to identify next-generation bio-geophysical variable retrieval algorithms which can be molded into an operational processing chain. This paper offers a review of state-of-the-art retrieval methods for quantitative terrestrial bio-geophysical variable extraction using op…

Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis

Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical explanations that do consider both phenomena simultaneously follow parametric formulations based on empirical models. Therefore, it may be argued that the behavior does not come directly from the color statistics but from the convenient functional form adopted. In addition, many times the whole statistical analysis is based on simplified databases that disregard relevant physical effects in the input signal, as, for instance…

Regularized multiresolution spatial unmixing for ENVISAT/MERIS and landsat/TM image fusion

Earth observation satellites currently provide a large volume of images at different scales. Most of these satellites provide global coverage with a revisit time that usually depends on the instrument characteristics and performance. Typically, medium-spatial-resolution instruments provide better spectral and temporal resolutions than mapping-oriented high-spatial-resolution multispectral sensors. However, in order to monitor a given area of interest, users demand images with the best resolution available, which cannot be reached using a single sensor. In this context, image fusion may be effective to merge information from different data sources. In this letter, an image fusion approach ba…

Kernel-Based Framework for Multitemporal and Multisource Remote Sensing Data Classification and Change Detection

The multitemporal classification of remote sensing images is a challenging problem, in which the efficient combination of different sources of information (e.g., temporal, contextual, or multisensor) can improve the results. In this paper, we present a general framework based on kernel methods for the integration of heterogeneous sources of information. Using the theoretical principles in this framework, three main contributions are presented. First, a novel family of kernel-based methods for multitemporal classification of remote sensing images is presented. The second contribution is the development of nonlinear kernel classifiers for the well-known difference and ratioing change detectio…

A unified vegetation index for quantifying the terrestrial biosphere

[EN] Empirical vegetation indices derived from spectral reflectance data are widely used in remote sensing of the biosphere, as they represent robust proxies for canopy structure, leaf pigment content, and, subsequently, plant photosynthetic potential. Here, we generalize the broad family of commonly used vegetation indices by exploiting all higher-order relations between the spectral channels involved. This results in a higher sensitivity to vegetation biophysical and physiological parameters. The presented nonlinear generalization of the celebrated normalized difference vegetation index (NDVI) consistently improves accuracy in monitoring key parameters, such as leaf area index, gross prim…

Kernel dependence regularizers and Gaussian processes with applications to algorithmic fairness

Current adoption of machine learning in industrial, societal and economical activities has raised concerns about the fairness, equity and ethics of automated decisions. Predictive models are often developed using biased datasets and thus retain or even exacerbate biases in their decisions and recommendations. Removing the sensitive covariates, such as gender or race, is insufficient to remedy this issue since the biases may be retained due to other related covariates. We present a regularization approach to this problem that trades off predictive accuracy of the learned models (with respect to biased labels) for the fairness in terms of statistical parity, i.e. independence of the decisions…

Sparse Deconvolution Using Support Vector Machines

Sparse deconvolution is a classical subject in digital signal processing, having many practical applications. Support vector machine (SVM) algorithms show a series of characteristics, such as sparse solutions and implicit regularization, which make them attractive for solving sparse deconvolution problems. Here, a sparse deconvolution algorithm based on the SVM framework for signal processing is presented and analyzed, including comparative evaluations of its performance from the points of view of estimation and detection capabilities, and of robustness with respect to non-Gaussian additive noise. Publicado

Joint Gaussian Processes for Biophysical Parameter Retrieval

Solving inverse problems is central to geosciences and remote sensing. Radiative transfer models (RTMs) represent mathematically the physical laws which govern the phenomena in remote sensing applications (forward models). The numerical inversion of the RTM equations is a challenging and computationally demanding problem, and for this reason, often the application of a nonlinear statistical regression is preferred. In general, regression models predict the biophysical parameter of interest from the corresponding received radiance. However, this approach does not employ the physical information encoded in the RTMs. An alternative strategy, which attempts to include the physical knowledge, co…

Sensitivity Maps of the Hilbert-Schmidt Independence Criterion

Abstract Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampered by two important problems: the high computational cost involved, as two kernel matrices of the sample size have to be computed and stored, and the interpretability of the measure, which remains hidden behind the implicit feature map. We here address these two issues. We introduce the sensitivity maps (SMs) for the Hilbert–Schmidt independence criterion (HSIC). Sensi…

Extraction Of Smos Soil Moisture And Ocean Salinity Main Features Across The Mediterranean Region Over The Last Decade

med 2018, 11-12 December 2018, Frascati, Rome, Italy

Large-scale random features for kernel regression

Kernel methods constitute a family of powerful machine learning algorithms, which have found wide use in remote sensing and geosciences. However, kernel methods are still not widely adopted because of the high computational cost when dealing with large scale problems, such as the inversion of radiative transfer models. This paper introduces the method of random kitchen sinks (RKS) for fast statistical retrieval of bio-geo-physical parameters. The RKS method allows to approximate a kernel matrix with a set of random bases sampled from the Fourier domain. We extend their use to other bases, such as wavelets, stumps, and Walsh expansions. We show that kernel regression is now possible for data…

Cloud masking and removal in remote sensing image time series

Automatic cloud masking of Earth observation images is one of the first required steps in optical remote sensing data processing since the operational use and product generation from satellite image time series might be hampered by undetected clouds. The high temporal revisit of current and forthcoming missions and the scarcity of labeled data force us to cast cloud screening as an unsupervised change detection problem in the temporal domain. We introduce a cloud screening method based on detecting abrupt changes along the time dimension. The main assumption is that image time series follow smooth variations over land (background) and abrupt changes will be mainly due to the presence of clo…

Efficient Kernel Cook's Distance for Remote Sensing Anomalous Change Detection

Detecting anomalous changes in remote sensing images is a challenging problem, where many approaches and techniques have been presented so far. We rely on the standard field of multivariate statistics of diagnostic measures, which are concerned about the characterization of distributions, detection of anomalies, extreme events, and changes. One useful tool to detect multivariate anomalies is the celebrated Cook's distance. Instead of assuming a linear relationship, we present a novel kernelized version of the Cook's distance to address anomalous change detection in remote sensing images. Due to the large computational burden involved in the direct kernelization, and the lack of out-…

Machine learning information fusion in Earth observation: A comprehensive review of methods, applications and data sources

This paper reviews the most important information fusion data-driven algorithms based on Machine Learning (ML) techniques for problems in Earth observation. Nowadays we observe and model the Earth with a wealth of observations, from a plethora of different sensors, measuring states, fluxes, processes and variables, at unprecedented spatial and temporal resolutions. Earth observation is well equipped with remote sensing systems, mounted on satellites and airborne platforms, but it also involves in-situ observations, numerical models and social media data streams, among other data sources. Data-driven approaches, and ML techniques in particular, are the natural choice to extract significant i…

Reply to Magnani et al.: Linking large-scale chlorophyll fluorescence observations with cropland gross primary production

Guanter, Luis et al.

A carbon sink-driven approach to estimate gross primary production from microwave satellite observations

Abstract Global estimation of Gross Primary Production (GPP) - the uptake of atmospheric carbon dioxide by plants through photosynthesis - is commonly based on optical satellite remote sensing data. This presents a source-driven approach since it uses the amount of absorbed light, the main driver of photosynthesis, as a proxy for GPP. Vegetation Optical Depth (VOD) estimates obtained from microwave sensors provide an alternative and independent data source to estimate GPP on a global scale, which may complement existing GPP products. Recent studies have shown that VOD is related to aboveground biomass, and that both VOD and temporal changes in VOD relate to GPP. In this study, we build upon…

Machine Learning Regression Approaches for Colored Dissolved Organic Matter (CDOM) Retrieval with S2-MSI and S3-OLCI Simulated Data

The colored dissolved organic matter (CDOM) variable is the standard measure of humic substance in waters optics. CDOM is optically characterized by its spectral absorption coefficient, a C D O M at at reference wavelength (e.g., ≈ 440 nm). Retrieval of CDOM is traditionally done using bio-optical models. As an alternative, this paper presents a comparison of five machine learning methods applied to Sentinel-2 and Sentinel-3 simulated reflectance ( R r s ) data for the retrieval of CDOM: regularized linear regression (RLR), random forest regression (RFR), kernel ridge regression (KRR), Gaussian process regression (GPR) and support vector machines (SVR). Two different datasets of radiative t…

Weakly supervised alignment of multisensor images

Manifold alignment has become very popular in recent literature. Aligning data distributions prior to product generation is an appealing strategy, since it allows to provide data spaces that are more similar to each other, regardless of the subsequent use of the transformed data. We propose a methodology that finds a common representation among data spaces from different sensors using geographic image correspondences, or semantic ties. To cope with the strong deformations between the data spaces considered, we propose to add nonlineari-ties by expanding the input space with Gaussian Radial Basis Function (RBF) features with respect to the centroids of a partitioning of the data. Such featur…

Global Groundwater-Vegetation Relations

Groundwater is an integral component of the water cycle, and it also influences the carbon cycle by supplying moisture to ecosystems. However, the extent and determinants of groundwater-vegetation interactions are poorly understood at the global scale. Using several high-resolution data products, we show that the spatial patterns of ecosystem gross primary productivity and groundwater table depth are correlated during at least one season in more than two-thirds of the global vegetated area. Positive relationships, i.e., larger productivity under shallower groundwater table, predominate in moisture-limited dry to mesic conditions with herbaceous and shrub vegetation. Negative relationships, …

Statistical retrieval of atmospheric profiles with deep convolutional neural networks

Abstract Infrared atmospheric sounders, such as IASI, provide an unprecedented source of information for atmosphere monitoring and weather forecasting. Sensors provide rich spectral information that allows retrieval of temperature and moisture profiles. From a statistical point of view, the challenge is immense: on the one hand, “underdetermination” is common place as regression needs to work on high dimensional input and output spaces; on the other hand, redundancy is present in all dimensions (spatial, spectral and temporal). On top of this, several noise sources are encountered in the data. In this paper, we present for the first time the use of convolutional neural networks for the retr…

Group Importance Sampling for particle filtering and MCMC

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discus…

Nonlinear statistical retrieval of surface emissivity from IASI data

Emissivity is one of the most important parameters to improve the determination of the troposphere properties (thermodynamic properties, aerosols and trace gases concentration) and it is essential to estimate the radiative budget. With the second generation of infrared sounders, we can estimate emissivity spectra at high spectral resolution, which gives us a global view and long-term monitoring of continental surfaces. Statistically, this is an ill-posed retrieval problem, with as many output variables as inputs. We here propose nonlinear multi-output statistical regression based on kernel methods to estimate spectral emissivity given the radiances. Kernel methods can cope with high-dimensi…

Efficient pruning of multilayer perceptrons using a fuzzy sigmoid activation function

This Letter presents a simple and powerful pruning method for multilayer feed forward neural networks based on the fuzzy sigmoid activation function presented in [E. Soria, J. Martin, G. Camps, A. Serrano, J. Calpe, L. Gomez, A low-complexity fuzzy activation function for artificial neural networks, IEEE Trans. Neural Networks 14(6) (2003) 1576-1579]. Successful performance is obtained in standard function approximation and channel equalization problems. Pruning allows to reduce network complexity considerably, achieving a similar performance to that obtained by unpruned networks.

Cloud detection for CHRIS/Proba hyperspectral images

Accurate and automatic detection of clouds in satellite scenes is a key issue for a wide range of remote sensing applications. With no accurate cloud masking, undetected clouds are one of the most significant source of error in both sea and land cover biophysical parameter retrieval. Sensors with spectral channels beyond 1 um have demonstrated good capabilities to perform cloud masking. This spectral range can not be exploited by recently developed hyperspectral sensors that work in the spectral range between 400- 1000 nm. However, one can take advantage of their high number of channels and spectral resolution to increase the cloud detection accuracy, and to describe properly the detected c…

Semisupervised Kernel Feature Extraction for Remote Sensing Image Analysis

This paper presents a novel semisupervised kernel partial least squares (KPLS) algorithm for nonlinear feature extraction to tackle both land-cover classification and biophysical parameter retrieval problems. The proposed method finds projections of the original input data that align with the target variable (labels) and incorporates the wealth of unlabeled information to deal with low-sized or underrepresented data sets. The method relies on combining two kernel functions: the standard radial-basis-function kernel based on labeled information and a generative, i.e., probabilistic, kernel directly learned by clustering the data many times and at different scales across the data manifold. Th…

A Deep Network Approach to Multitemporal Cloud Detection

We present a deep learning model with temporal memory to detect clouds in image time series acquired by the Seviri imager mounted on the Meteosat Second Generation (MSG) satellite. The model provides pixel-level cloud maps with related confidence and propagates information in time via a recurrent neural network structure. With a single model, we are able to outline clouds along all year and during day and night with high accuracy.

Experimental Sentinel-2 LAI estimation using parametric, non-parametric and physical retrieval methods – A comparison

Abstract Given the forthcoming availability of Sentinel-2 (S2) images, this paper provides a systematic comparison of retrieval accuracy and processing speed of a multitude of parametric, non-parametric and physically-based retrieval methods using simulated S2 data. An experimental field dataset (SPARC), collected at the agricultural site of Barrax (Spain), was used to evaluate different retrieval methods on their ability to estimate leaf area index (LAI). With regard to parametric methods, all possible band combinations for several two-band and three-band index formulations and a linear regression fitting function have been evaluated. From a set of over ten thousand indices evaluated, the …

Distributed Particle Metropolis-Hastings Schemes

We introduce a Particle Metropolis-Hastings algorithm driven by several parallel particle filters. The communication with the central node requires the transmission of only a set of weighted samples, one per filter. Furthermore, the marginal version of the previous scheme, called Distributed Particle Marginal Metropolis-Hastings (DPMMH) method, is also presented. DPMMH can be used for making inference on both a dynamical and static variable of interest. The ergodicity is guaranteed, and numerical simulations show the advantages of the novel schemes.

Encoding Invariances in Remote Sensing Image Classification With SVM

This letter introduces a simple method for including invariances in support-vector-machine (SVM) remote sensing image classification. We design explicit invariant SVMs to deal with the particular characteristics of remote sensing images. The problem of including data invariances can be viewed as a problem of encoding prior knowledge, which translates into incorporating informative support vectors (SVs) that better describe the classification problem. The proposed method essentially generates new (synthetic) SVs from the obtained by training a standard SVM with the available labeled samples. Then, original and transformed SVs are used for training the virtual SVM introduced in this letter. W…

Quantifying uncertainty in high resolution biophysical variable retrieval with machine learning

The estimation of biophysical variables is at the core of remote sensing science, allowing a close monitoring of crops and forests. Deriving temporally resolved and spatially explicit maps of parameters of interest has been the subject of intense research. However, deriving products from optical sensors is typically hampered by cloud contamination and the trade-off between spatial and temporal resolutions. In this work we rely on the HIghly Scalable Temporal Adaptive Reflectance Fusion Model (HISTARFM) algorithm to generate long gap-free time series of Landsat surface reflectance data by fusing MODIS and Landsat reflectances. An artificial neural network is trained on PROSAIL inversion to p…

Fusing optical and SAR time series for LAI gap filling with multioutput Gaussian processes

The availability of satellite optical information is often hampered by the natural presence of clouds, which can be problematic for many applications. Persistent clouds over agricultural fields can mask key stages of crop growth, leading to unreliable yield predictions. Synthetic Aperture Radar (SAR) provides all-weather imagery which can potentially overcome this limitation, but given its high and distinct sensitivity to different surface properties, the fusion of SAR and optical data still remains an open challenge. In this work, we propose the use of Multi-Output Gaussian Process (MOGP) regression, a machine learning technique that learns automatically the statistical relationships among…

Group Metropolis Sampling

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. Two well-known class of MC methods are the Importance Sampling (IS) techniques and the Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce the Group Importance Sampling (GIS) framework where different sets of weighted samples are properly summarized with one summary particle and one summary weight. GIS facilitates the design of novel efficient MC techniques. For instance, we present the Group Metropolis Sampling (GMS) algorithm which produces a Markov chain of sets of weighted samples. GMS in general outperforms other multiple try schemes…

Machine learning regression algorithms for biophysical parameter retrieval: Opportunities for Sentinel-2 and -3

Abstract ESA's upcoming satellites Sentinel-2 (S2) and Sentinel-3 (S3) aim to ensure continuity for Landsat 5/7, SPOT-5, SPOT-Vegetation and Envisat MERIS observations by providing superspectral images of high spatial and temporal resolution. S2 and S3 will deliver near real-time operational products with a high accuracy for land monitoring. This unprecedented data availability leads to an urgent need for developing robust and accurate retrieval methods. Machine learning regression algorithms may be powerful candidates for the estimation of biophysical parameters from satellite reflectance measurements because of their ability to perform adaptive, nonlinear data fitting. By using data from …

Passive millimeter wave image classification with large scale Gaussian processes

Passive Millimeter Wave Images (PMMWIs) are being increasingly used to identify and localize objects concealed under clothing. Taking into account the quality of these images and the unknown position, shape, and size of the hidden objects, large data sets are required to build successful classification/detection systems. Kernel methods, in particular Gaussian Processes (GPs), are sound, flexible, and popular techniques to address supervised learning problems. Unfortunately, their computational cost is known to be prohibitive for large scale applications. In this work, we present a novel approach to PMMWI classification based on the use of Gaussian Processes for large data sets. The proposed…

Fair Kernel Learning

New social and economic activities massively exploit big data and machine learning algorithms to do inference on people's lives. Applications include automatic curricula evaluation, wage determination, and risk assessment for credits and loans. Recently, many governments and institutions have raised concerns about the lack of fairness, equity and ethics in machine learning to treat these problems. It has been shown that not including sensitive features that bias fairness, such as gender or race, is not enough to mitigate the discrimination when other related features are included. Instead, including fairness in the objective function has been shown to be more efficient. We present novel fai…

Therapeutic Drug Monitoring of Kidney Transplant Recipients Using Profiled Support Vector Machines

This paper proposes a twofold approach for therapeutic drug monitoring (TDM) of kidney recipients using support vector machines (SVMs), for both predicting and detecting Cyclosporine A (CyA) blood concentrations. The final goal is to build useful, robust, and ultimately understandable models for individualizing the dosage of CyA. We compare SVMs with several neural network models, such as the multilayer perceptron (MLP), the Elman recurrent network, finite/infinite impulse response networks, and neural network ARMAX approaches. In addition, we present a profile-dependent SVM (PD-SVM), which incorporates a priori knowledge in both tasks. Models are compared numerically, statistically, and in…

A perspective on Gaussian processes for Earth observation

Earth observation (EO) by airborne and satellite remote sensing and in-situ observations play a fundamental role in monitoring our planet. In the last decade, machine learning and Gaussian processes (GPs) in particular has attained outstanding results in the estimation of bio-geo-physical variables from the acquired images at local and global scales in a time-resolved manner. GPs provide not only accurate estimates but also principled uncertainty estimates for the predictions, can easily accommodate multimodal data coming from different sensors and from multitemporal acquisitions, allow the introduction of physical knowledge, and a formal treatment of uncertainty quantification and error pr…

Machine Learning Methods for Spatial and Temporal Parameter Estimation

Monitoring vegetation with satellite remote sensing is of paramount relevance to understand the status and health of our planet. Accurate and constant monitoring of the biosphere has large societal, economical, and environmental implications, given the increasing demand of biofuels and food by the world population. The current democratization of machine learning, big data, and high processing capabilities allow us to take such endeavor in a decisive manner. This chapter proposes three novel machine learning approaches to exploit spatial, temporal, multi-sensor, and large-scale data characteristics. We show (1) the application of multi-output Gaussian processes for gap-filling time series of…

Latent force models for earth observation time series prediction

We introduce latent force models for Earth observation time series analysis. The model uses Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. The LFM presented here performs multi-output structured regression, adapts to the signal characteristics, it can cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. We successfully illustrate the performance in challenging scenarios of crop monitoring from space, providing time-resolved time series predictions.

Retrieval of coloured dissolved organic matter with machine learning methods

The coloured dissolved organic matter (CDOM) concentration is the standard measure of humic substance in natural waters. CDOM measurements by remote sensing is calculated using the absorption coefficient (a) at a certain wavelength (e.g. 440nm). This paper presents a comparison of four machine learning methods for the retrieval of CDOM from remote sensing signals: regularized linear regression (RLR), random forest (RF), kernel ridge regression (KRR) and Gaussian process regression (GPR). Results are compared with the established polynomial regression algorithms. RLR is revealed as the simplest and most efficient method, followed closely by its nonlinear counterpart KRR.

Unbiased sensitivity analysis and pruning techniques in neural networks for surface ozone modelling

Abstract This paper presents the use of artificial neural networks (ANNs) for surface ozone modelling. Due to the usual non-linear nature of problems in ecology, the use of ANNs has proven to be a common practice in this field. Nevertheless, few efforts have been made to acquire knowledge about the problems by analysing the useful, but often complex, input–output mapping performed by these models. In fact, researchers are not only interested in accurate methods but also in understandable models. In the present paper, we propose a methodology to extract the governing rules of trained ANN which, in turn, yields simplified models by using unbiased sensitivity and pruning techniques. Our propos…

Gap Filling of Biophysical Parameter Time Series with Multi-Output Gaussian Processes

In this work we evaluate multi-output (MO) Gaussian Process (GP) models based on the linear model of coregionalization (LMC) for estimation of biophysical parameter variables under a gap filling setup. In particular, we focus on LAI and fAPAR over rice areas. We show how this problem cannot be solved with standard single-output (SO) GP models, and how the proposed MO-GP models are able to successfully predict these variables even in high missing data regimes, by implicitly performing an across-domain information transfer.

Gross Primary Production and false spring: a spatio-temporal analysis

<p>Phenological information can be obtained from different sources of data. For instance, from remote sensing data or products and from models driven by weather variables. The former typically allows analyzing land surface phenology whereas the latter provide plant phenological information. Analyzing relationships between both sources of data allows us to understand the impact of climate change on vegetation over space and time. For example, the onset of spring is advanced or delayed by changes in the climate. These alterations affect plant productivity and animal migrations.</p><p>Spring onset monitoring is supported by the Extended Spring Index (…

Including invariances in SVM remote sensing image classification

This paper introduces a simple method to include invariances in support vector machine (SVM) for remote sensing image classification. We rely on the concept of virtual support vectors, by which the SVM is trained with both the selected support vectors and synthetic examples encoding the invariance of interest. The algorithm is very simple and effective, as demonstrated in two particularly interesting examples: invariance to the presence of shadows and to rotations in patchbased image segmentation. The improved accuracy (around +6% both in OA and Cohen's κ statistic), along with the simplicity of the approach encourage its use and extension to encode other invariances and other remote sensin…

Warped Gaussian Processes in Remote Sensing Parameter Estimation and Causal Inference

This letter introduces warped Gaussian process (WGP) regression in remote sensing applications. WGP models output observations as a parametric nonlinear transformation of a GP. The parameters of such a prior model are then learned via standard maximum likelihood. We show the good performance of the proposed model for the estimation of oceanic chlorophyll content from multispectral data, vegetation parameters (chlorophyll, leaf area index, and fractional vegetation cover) from hyperspectral data, and in the detection of the causal direction in a collection of 28 bivariate geoscience and remote sensing causal problems. The model consistently performs better than the standard GP and the more a…

Inferring causation from time series in earth system sciences

The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers.

Semisupervised nonlinear feature extraction for image classification

Feature extraction is of paramount importance for an accurate classification of remote sensing images. Techniques based on data transformations are widely used in this context. However, linear feature extraction algorithms, such as the principal component analysis and partial least squares, can address this problem in a suboptimal way because the data relations are often nonlinear. Kernel methods may alleviate this problem only when the structure of the data manifold is properly captured. However, this is difficult to achieve when small-size training sets are available. In these cases, exploiting the information contained in unlabeled samples together with the available training data can si…

Probabilistic cross-validation estimators for Gaussian process regression

Gaussian Processes (GPs) are state-of-the-art tools for regression. Inference of GP hyperparameters is typically done by maximizing the marginal log-likelihood (ML). If the data truly follows the GP model, using the ML approach is optimal and computationally efficient. Unfortunately very often this is not case and suboptimal results are obtained in terms of prediction error. Alternative procedures such as cross-validation (CV) schemes are often employed instead, but they usually incur in high computational costs. We propose a probabilistic version of CV (PCV) based on two different model pieces in order to reduce the dependence on a specific model choice. PCV presents the benefits from both…

Sensitivity Maps of the Hilbert-Schmidt Independence Criterion

Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampered by two important problems: the high computational cost involved, as two kernel matrices of the sample size have to be computed and stored, and the interpretability of the measure, which remains hidden behind the implicit feature map. We here address these two issues. We introduce the Sensitivity Maps (SMs) for the Hilbert-Schmidt independence criterion (HSIC). Sensitivity ma…

Dimensionality Reduction via Regression in Hyperspectral Imagery

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between he PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservation, and straightforward out-of-sample extension, makes DRR interpretable and easy to apply. The pro…

Hyperspectral system for early detection of rottenness caused by Penicillium digitatum in mandarins

Abstract Nowadays, the detection of fruit infected with Penicillium sp. fungi on packing lines is carried out manually under ultraviolet illumination. Ultraviolet sources induce visible fluorescence of essential oils, present in the skin of citrus and which are released by the action of fungi, thus increasing the contrast between sound and rotten skin. This work analyses a set of techniques aimed at detecting rotten citrus without the use of UV lighting. The techniques used include hyperspectral image acquisition, pre-processing and calibration, feature selection and segmentation using linear and non-linear methods for classification of fruits. Different methods such as correlation analysis…

Machine learning in remote sensing data processing

Remote sensing data processing deals with real-life applications with great societal values. For instance urban monitoring, fire detection or flood prediction from remotely sensed multispectral or radar images have a great impact on economical and environmental issues. To treat efficiently the acquired data and provide accurate products, remote sensing has evolved into a multidisciplinary field, where machine learning and signal processing algorithms play an important role nowadays. This paper serves as a survey of methods and applications, and reviews the latest methodological advances in machine learning for remote sensing data analysis.

Semi-Supervised Support Vector Biophysical Parameter Estimation

Two kernel-based methods for semi-supervised regression are presented. The methods rely on building a graph or hypergraph Laplacian with both the labeled and unlabeled data, which is further used to deform the training kernel matrix. The deformed kernel is then used for support vector regression (SVR). The semi-supervised SVR methods are sucessfully tested in LAI estimation and ocean chlorophyll concentration prediction from remotely sensed images.

Automatic correction of the effects of the light source on spherical objects. An application to the analysis of hyperspectral images of citrus fruits

This study proposes a method for correcting the adverse effects produced by the curvature of spherical objects in acquiring images with a computer vision system. Its suitability has been illustrated in a specific case of citrus fruits. The images of this kind of fruit are darker in areas nearer the edge than in the centre, and this makes them more difficult to analyse. This methodology considers the fruit as being a Lambertian ellipsoidal surface and produces a 3D model of the fruit. By doing it becomes possible to calculate the part of the radiation that should really reach the camera and to make the intensity of the radiation uniform over the whole of the fruit surface captured by the cam…

Multitemporal Cloud Masking in the Google Earth Engine

The exploitation of Earth observation satellite images acquired by optical instruments requires an automatic and accurate cloud detection. Multitemporal approaches to cloud detection are usually more powerful than their single scene counterparts since the presence of clouds varies greatly from one acquisition to another whereas surface can be assumed stationary in a broad sense. However, two practical limitations usually hamper their operational use: the access to the complete satellite image archive and the required computational power. This work presents a cloud detection and removal methodology implemented in the Google Earth Engine (GEE) cloud computing platform in order to meet these r…

Cluster kernels for semisupervised classification of VHR urban images

In this paper, we present and apply a semisupervised support vector machine based on cluster kernels for the problem of very high resolution image classification. In the proposed setting, a base kernel working with labeled samples only is deformed by a likelihood kernel encoding similarities between unlabeled examples. The resulting kernel is used to train a standard support vector machine (SVM) classifier. Experiments carried out on very high resolution (VHR) multispectral and hyperspectral images using very few labeled examples show the relevancy of the method in the context of urban image classification. Its simplicity and the small number of parameters involved make it versatile and wor…

HyperLabelMe : A Web Platform for Benchmarking Remote-Sensing Image Classifiers

HyperLabelMe is a web platform that allows the automatic benchmarking of remote-sensing image classifiers. To demonstrate this platform's attributes, we collected and harmonized a large data set of labeled multispectral and hyperspectral images with different numbers of classes, dimensionality, noise sources, and levels. The registered user can download training data pairs (spectra and land cover/use labels) and submit the predictions for unseen testing spectra. The system then evaluates the accuracy and robustness of the classifier, and it reports different scores as well as a ranked list of the best methods and users. The system is modular, scalable, and ever-growing in data sets and clas…

Upport vector machines for nonlinear kernel ARMA system identification.

Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA 2k) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based syste…

Learning Structures in Earth Observation Data with Gaussian Processes

Gaussian Processes (GPs) has experienced tremendous success in geoscience in general and for bio-geophysical parameter retrieval in the last years. GPs constitute a solid Bayesian framework to formulate many function approximation problems consistently. This paper reviews the main theoretical GP developments in the field. We review new algorithms that respect the signal and noise characteristics, that provide feature rankings automatically, and that allow applicability of associated uncertainty intervals to transport GP models in space and time. All these developments are illustrated in the field of geoscience and remote sensing at a local and global scales through a set of illustrative exa…

Perceptual adaptive insensitivity for support vector machine image coding.

Support vector machine (SVM) learning has been recently proposed for image compression in the frequency domain using a constant epsilon-insensitivity zone by Robinson and Kecman. However, according to the statistical properties of natural images and the properties of human perception, a constant insensitivity makes sense in the spatial domain but it is certainly not a good option in a frequency domain. In fact, in their approach, they made a fixed low-pass assumption as the number of discrete cosine transform (DCT) coefficients to be used in the training was limited. This paper extends the work of Robinson and Kecman by proposing the use of adaptive insensitivity SVMs [2] for image coding u…

Traitement de données RGB et Lidar à extrêmement haute résolution: retombées de la compétition de fusion de données 2015 de l'IEEE GRSS - Partie A / compétition 2D

International audience; In this paper, we discuss the scientific outcomes of the 2015 data fusion contest organized by the Image Analysis and Data Fusion Technical Committee (IADF TC) of the IEEE Geoscience and Remote Sensing Society (IEEE GRSS). As for previous years, the IADF TC organized a data fusion contest aiming at fostering new ideas and solutions for multisource studies. The 2015 edition of the contest proposed a multiresolution and multisensorial challenge involving extremely high-resolution RGB images and a three-dimensional (3-D) LiDAR point cloud. The competition was framed in two parallel tracks, considering 2-D and 3-D products, respectively. In this paper, we discuss the sci…

Kernel image similarity criterion

This paper presents a family of metrics for assessing image similarity. The methods use the Hilbert-Schmidt Independence Criterion (HSIC) to estimate nonlinear statistical dependence between multidimensional images. The proposed methods have very good theoretical and practical properties. We illustrate the performance in evaluating the quality of natural photographic images, hyperspectral images under different noise levels, in synthetic multiresolution problems, and real pansharpening products.

Efficient remote sensing image classification with Gaussian processes and Fourier features

This paper presents an efficient methodology for approximating kernel functions in Gaussian process classification (GPC). Two models are introduced. We first include the standard random Fourier features (RFF) approximation into GPC, which largely improves the computational efficiency and permits large scale remote sensing data classification. In addition, we develop a novel approach which avoids randomly sampling a number of Fourier frequencies, and alternatively learns the optimal ones using a variational Bayes approach. The performance of the proposed methods is illustrated in complex problems of cloud detection from multispectral imagery.

Global Cropland Yield Monitoring with Gaussian Processes

Agriculture monitoring, and in particular food security, requires near real-time information on crop growing conditions for early detection of possible production deficits. In this work, we propose the use of Gaussian processes (GPs). together with in-situ, EO and ERA-Interim climate reanalysis data for crop yield forecasting. Country-level agricultural survey data from FAOSTAT are used for quantitative assessment. The study is conducted in the framework of the ASAP (Anomaly hot Spots of Agricultural Production) early warning decision support system of the European Commission, which aims at providing timely information about possible crop production anomalies worldwide. After grouping count…

Multi-fidelity Gaussian Process Emulation for Atmospheric Radiative Transfer Models

This repository contains several datasets of spectral atmospheric transfer functions (i.e. path radiance, transmittances, spherical albedo) simulated with MODTRAN6 atmospheric radiative transfer model. The simulations are stored in hdf5 files using the Atmospheric Look-up table Generator (ALG) toolbox (https://doi.org/10.5194/gmd-13-1945-2020). Each dataset has an associated .xml file that includes the configuration of ALG/MODTRAN6 executions. All datasets include the input atmospheric/geometric variables that are summarized in the following table. Each dataset file has a random distribution (based on latin hypercube sampling) these input variables with varying number of points (e.g. train5…

IASI dataset v1

The Infrared Atmospheric Sounding Interferometer (IASI) on board the MetOp satellite series measures the infrared spectrum with high resolution. The ground footprint resolution of the instruments is 12 km at nadir, and a spectral resolution of 0.25cm −1 in the spectrum between 645 cm −1 and 2760 cm −1 . This results in 8461 spectral samples covering 2200km scan-swath with 60 points per line. IASI is an ideal instrument for monitoring different physical/chemical parameters in the atmosphere e.g. temperature, humidity and trace gases such as ozone. Energy from different altitudes returns a different spectral shift. In this way atmospheric profiles can be obtained and these provides important …

Revisiting impacts of MJO on soil moisture: a causality perspective

Tratamiento digital de señales. Problemas y ejercicios resueltos

El documento es un libro de problemas y ejercicios de Tratamiento Digital de Señales. Este libro publicado por Prentice-Hall en 2003, se ofrece actualmente como recurso de acceso abierto tras su descatalogación. En él se ofrecen ejemplos de problemas y ejercicios resueltos de Tratamiento Digital de Señales, a los que previamente se introduce la base teórica suficiente como para seguir el desarrollo del texto. El contenido es el siguiente: Señales y sistemas en tiempo discreto; Análisis frecuencial de señales y sistemas; Transformada z; Realización de sistemas en tiempo discreto; Efectos de longitud de palabra finita; Diseño de filtros digitales; Sistemas adaptativos. That document is a book…

Gap Filling of Biophysical Parameter Time Series with Multi-Output Gaussian Processes

In this work we evaluate multi-output (MO) Gaussian Process (GP) models based on the linear model of coregionalization (LMC) for estimation of biophysical parameter variables under a gap filling setup. In particular, we focus on LAI and fAPAR over rice areas. We show how this problem cannot be solved with standard single-output (SO) GP models, and how the proposed MO-GP models are able to successfully predict these variables even in high missing data regimes, by implicitly performing an across-domain information transfer. CICYT TIN2015-64210-R In this work we evaluate multi-output (MO) Gaussian Process (GP) models based on the linear model of coregionalization (LMC) for estimation of biophy…