Search results for "transforms"
showing 10 items of 40 documents
Identification of Objects Based on Generalized Amplitude-Phase Images Statistical Models
2017
The article presents the dynamical objects identification technology based on statistical models of amplitude-phase images (APIm) – multidimensional data arrays (semantic models) and statistical correlation analysis methods using the generalized discrete Hilbert transforms (DHT) – 2D Hilbert (Foucault) isotropic (HTI), anisotropic (HTA) and total transforms – AP-analysis (APA) to calculate the APIm. The identified objects are modeled with 3D airplanes templates rotated in space around the center of Cartesian coordinate system. The DHT domain system of coordinates displaying the plane projections (2D flat images) remains to be space-invariant. That causes the anisotropic properties of APIm a…
Measuring spectrally-resolved information transfer.
2020
Information transfer, measured by transfer entropy, is a key component of distributed computation. It is therefore important to understand the pattern of information transfer in order to unravel the distributed computational algorithms of a system. Since in many natural systems distributed computation is thought to rely on rhythmic processes a frequency resolved measure of information transfer is highly desirable. Here, we present a novel algorithm, and its efficient implementation, to identify separately frequencies sending and receiving information in a network. Our approach relies on the invertible maximum overlap discrete wavelet transform (MODWT) for the creation of surrogate data in t…
Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds
2017
We study ray transforms on spherically symmetric manifolds with a piecewise $C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2$ functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a $C^{1,1}$ metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.
Phase information of time-frequency transforms as a key feature for classification of atrial fibrillation episodes
2015
[EN] Patients suffering from atrial fibrillation can be classified into different subtypes, according to the temporal pattern of the arrhythmia and its recurrence. Nowadays, clinicians cannot differentiate a priori between the different subtypes, and patient classification is done afterwards, when its clinical course is available. In this paper we present a comparison of classification performances when differentiating paroxysmal and persistent atrial fibrillation episodes by means of support vector machines. We analyze short surface electrocardiogram recordings by extracting modulus and phase features from several time-frequency transforms: short-time Fourier transform, Wigner-Ville, Choi-…
Noise reduction in magnetic resonance images by Wavelet transforms: an application to the study of capillary water absorption in sedimentary rocks
2007
Magnetic resonance imaging (MRI) is a powerful technique to study capillary water absorption kinetics in sedimentary rocks. However, the noise in the images can limit the correct identification and the quantitative measurement of the average height reached by the wetting front inside the porous material where imbibition occurs. Therefore, denoising methods can be applied to improve the image quality for a more accurate analysis, without the disadvantages of longer acquisition times. This study attempts to improve the signal-to-noise ratio of the images acquired by MRI on a sedimentary rock (Pietra di Lecce) using a waveletbased thresholding technique. The idea is to average some slightly di…
Low-Rate Reduced Complexity Image Compression using Directionlets
2006
The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) discontinuities, like edges and contours, that are anisotropic and characterized by geometrical regularity along different directions. In our previous work, we proposed a construction of critically sampled perfect reconstruction anisotropic transform with directional vanishing moments (DVM) imposed in the corresponding basis functions, called directionlets. Here, we show that the computational complexity of our transform is comparable to the co…
Sorting of Single Biomolecules based on Fourier Polar Representation of Surface Enhanced Raman Spectra
2016
AbstractSurface enhanced Raman scattering (SERS) spectroscopy becomes increasingly used in biosensors for its capacity to detect and identify single molecules. In practice, a large number of SERS spectra are acquired and reliable ranking methods are thus essential for analysing all these data. Supervised classification strategies, which are the most effective methods, are usually applied but they require pre-determined models or classes. In this work, we propose to sort SERS spectra in unknown groups with an alternative strategy called Fourier polar representation. This non-fitting method based on simple Fourier sine and cosine transforms produces a fast and graphical representation for sor…
Improved Statistically Based Retrievals via Spatial-Spectral Data Compression for IASI Data
2019
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…
Sparse Image Representation by Directionlets
2010
Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertical directions. One-dimensional discontinuities in images (edges or contours), which are important elements in visual perception, intersect too many wavelet basis functions and lead to a non-sparse representation. To capture efficiently these elongated structures characterized by geometrical regularity along different directions (not only the horizontal and vertical), a more complex multidirectional (M-DIR) and asymmetric transform is requi…
Discrete wavelet transform based multispectral filter array demosaicking
2013
International audience; The idea of colour filter array may be adapted to multi-spectral image acquisition by integrating more filter types into the array, and developing associated demosaicking algorithms. Several methods employing discrete wavelet transform (DWT) have been proposed for CFA demosaicking. In this work, we put forward an extended use of DWT for mul-tispectral filter array demosaicking. The extension seemed straightforward, however we observed striking results. This work contributes to better understanding of the issue by demonstrating that spectral correlation and spatial resolution of the images exerts a crucial influence on the performance of DWT based demosaicking.