Search results for "Gaussian"
showing 10 items of 652 documents
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
2012
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…
Band gap of corundumlike α−Ga2O3 determined by absorption and ellipsometry
2017
The electronic structure near the band gap of the corundumlike $\ensuremath{\alpha}$ phase of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ has been investigated by means of optical absorption and spectroscopic ellipsometry measurements in the ultraviolet (UV) range (400--190 nm). The absorption coefficient in the UV region and the imaginary part of the dielectric function exhibit two prominent absorption thresholds with wide but well-defined structures at 5.6 and 6.3 eV which have been ascribed to allowed direct transitions from crystal-field split valence bands to the conduction band. Excitonic effects with large Gaussian broadening are taken into account through the Elliott-Toyozawa model, which y…
Efficiency of gyrotrons with a tapered magnetic field in the regime of soft self-excitation
2018
As a rule, gyrotron operation with high efficiency is realized in the regime of hard self-excitation that requires a special start-up scenario: either a tuning of the external magnetic field or providing certain relations between mod-anode and beam voltages. This paper describes a study of gyrotron operation in slightly tapered external magnetic fields. It is shown how the use of tapered magnetic fields affects the maximum efficiency realizable in hard and soft excitation regimes. First, a model of gyrotron with the Gaussian axial profile of the resonator field is studied. Then, a similar treatment is done for a realistic resonator designed for a 140 GHz Karlsruhe Institute for Technology g…
Joint Gaussian processes for inverse modeling
2017
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…
Automatic emulator and optimized look-up table generation for radiative transfer models
2017
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…
Multioutput Automatic Emulator for Radiative Transfer Models
2018
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…
Optimal modalities for radiative transfer-neural network estimation of canopy biophysical characteristics: Evaluation over an agricultural area with …
2011
International audience; Neural networks trained over radiative transfer simulations constitute the basis of several operational algorithms to estimate canopy biophysical variables from satellite reflectance measurements. However, only little attention was paid to the training process which has a major impact on retrieval performances. This study focused on the several modalities of the training process within neural network estimation of LAI, FCOVER and FAPAR biophysical variables. Performances were evaluated over both actual experimental observations and model simulations. The SAIL and PROSPECT radiative transfer models were used here to simulate the training and the synthetic test dataset…
Efficient remote sensing image classification with Gaussian processes and Fourier features
2017
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.
Hyperspectral dimensionality reduction for biophysical variable statistical retrieval
2017
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…
Optimizing Gaussian Process Regression for Image Time Series Gap-Filling and Crop Monitoring
2020
Image processing entered the era of artificial intelligence, and machine learning algorithms emerged as attractive alternatives for time series data processing. Satellite image time series processing enables crop phenology monitoring, such as the calculation of start and end of season. Among the promising algorithms, Gaussian process regression (GPR) proved to be a competitive time series gap-filling algorithm with the advantage of, as developed within a Bayesian framework, providing associated uncertainty estimates. Nevertheless, the processing of time series images becomes computationally inefficient in its standard per-pixel usage, mainly for GPR training rather than the fitting step. To…