Modelling SAR with a Generalisation of the Rayleigh Distribution

Synthetic aperture radar (SAR) imagery has found important applications since its introduction, due to its clear advantage over optical satellite imagery, being operable in various weather conditions. However, due to the physics of radar imaging process, sar images contain unwanted artefacts in the form of a granular look which is called speckle. the assumptions of the classical SAR image generation model lead to the convention that the real and imaginary parts of the received wave follow a Gaussian law, which in turn means that the amplitude of the wave has a Rayleigh distribution- . However, some experimental data show impulsive characteristics which correspond to underlying heavy-tailed distributions, clearly non-rayleigh. some alternative distributions have been suggested such as weibull and log-normal distributions, however, in most of the cases these models are empirical, not derived with the consideration of underlying physical conditions and therefore are case specific. In this report, relaxing some of the assumptions leading to the classical rayleigh model and using the recent results in the literature on $\alpha$-stable distributions, we develop a generalised (heavy-tailed) version of the rayleigh model based on the assumption that the real and the imaginary parts of the received signal follows an isotropic $\alpha$-stable law which is suggested by a generalised form of the central limit theorem. we also derive novel methods for the estimation of the heavy-tailed rayleigh distribution parameter- s based on negative fractional-order statistics for model fitting. our experimental results show that the heavy-tailed rayleigh model can describe a wide range of data which could not be described by the classical rayleigh model

Using generic order moments for separation of dependent sources with linear conditional expectations

In this work, we approach the blind separation of dependent sources based only on a set of their linear mixtures. We prove that, when the sources have a pairwise dependence characterized by the linear conditional expectation (LCE) law, we are able to separate them by maximizing or minimizing a Generic Order Moment (GOM) of their mixture. This general measure includes the higher order as well as the fractional moment cases. Our results, not only confirm some of the existing results for the independent sources case but also they allow us to explore new objective functions for Dependent Component Analysis. A set of examples illustrating the consequences of our theory is presented. Also, a comparison of our GOM based algorithm, the classical FASTICA and a very recently proposed algorithm for dependent sources, the Bounded Component Analysis (BCA) algorithm, is shown.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Kuruoglu, Ercan E.. Istituto di Scienza e Tecnologie dell’Informazione; Italia. Consiglio Nazionale delle Ricerche; Italia21ª European Signal Processing ConferenceMarrakechMarruecosEuropean Signal Processing Society (EURASIP

A Generalized Gaussian Extension to the Rician Distribution for SAR Image Modeling

In this paper, we present a novel statistical model, $\textit{the generalized-Gaussian-Rician}$ (GG-Rician) distribution, for the characterization of synthetic aperture radar (SAR) images. Since accurate statistical models lead to better results in applications such as target tracking, classification, or despeckling, characterizing SAR images of various scenes including urban, sea surface, or agricultural, is essential. The proposed statistical model is based on the Rician distribution to model the amplitude of a complex SAR signal, the in-phase and quadrature components of which are assumed to be generalized-Gaussian distributed. The proposed amplitude GG-Rician model is further extended to cover the intensity SAR signals. In the experimental analysis, the GG-Rician model is investigated for amplitude and intensity SAR images of various frequency bands and scenes in comparison to state-of-the-art statistical models that include $\mathcal{K}$, Weibull, Gamma, and Lognormal. In order to decide on the most suitable model, statistical significance analysis via Kullback-Leibler divergence and Kolmogorov-Smirnov statistics are performed. The results demonstrate the superior performance and flexibility of the proposed model for all frequency bands and scenes and its applicability on both amplitude and intensity SAR images.Comment: 20 Pages, 9 figures, 8 table

Modelling SAR with a Generalisation of the Rayleigh Distribution

Synthetic aperture radar (SAR) imagery has found important applications since its introduction, due to its clear advantage over optical satellite imagery, being operable in various weather conditions. However, due to the physics of radar imaging process, sar images contain unwanted artefacts in the form of a granular look which is called speckle. the assumptions of the classical SAR image generation model lead to the convention that the real and imaginary parts of the received wave follow a Gaussian law, which in turn means that the amplitude of the wave has a Rayleigh distribution- . However, some experimental data show impulsive characteristics which correspond to underlying heavy-tailed distributions, clearly non-rayleigh. some alternative distributions have been suggested such as weibull and log-normal distributions, however, in most of the cases these models are empirical, not derived with the consideration of underlying physical conditions and therefore are case specific. In this report, relaxing some of the assumptions leading to the classical rayleigh model and using the recent results in the literature on $\alpha$-stable distributions, we develop a generalised (heavy-tailed) version of the rayleigh model based on the assumption that the real and the imaginary parts of the received signal follows an isotropic $\alpha$-stable law which is suggested by a generalised form of the central limit theorem. we also derive novel methods for the estimation of the heavy-tailed rayleigh distribution parameter- s based on negative fractional-order statistics for model fitting. our experimental results show that the heavy-tailed rayleigh model can describe a wide range of data which could not be described by the classical rayleigh model

Generalized Bayesian model selection for speckle on remote sensing images

Synthetic aperture radar (SAR) and ultrasound (US) are two important active imaging techniques for remote sensing, both of which are subject to speckle noise caused by coherent summation of back-scattered waves and subsequent nonlinear envelope transformations. Estimating the characteristics of this multiplicative noise is crucial to develop denoising methods and to improve statistical inference from remote sensing images. In this paper, reversible jump Markov chain Monte Carlo (RJMCMC) algorithm has been used with a wider interpretation and a recently proposed RJMCMC-based Bayesian approach, trans-space RJMCMC, has been utilized. The proposed method provides an automatic model class selection mechanism for remote sensing images of SAR and US where the model class space consists of popular envelope distribution families. The proposed method estimates the correct distribution family, as well as the shape and the scale parameters, avoiding performing an exhaustive search. For the experimental analysis, different SAR images of urban, forest and agricultural scenes, and two different US images of a human heart have been used. Simulation results show the efficiency of the proposed method in finding statistical models for speckle

Cauchy-Rician model for backscattering in urban SAR images

This paper presents a new statistical model for urban scene SAR images by combining the Cauchy distribution, which is heavy-tailed, with the Rician back-scattering. The literature spans various well-known models most of which are derived under the assumption that the scene consists of multitudes of random reflectors. This idea specifically fails for urban scenes since they accommodate a heterogeneous collection of strong scatterers such as buildings, cars, wall corners. Moreover, when it comes to analysing their statistical behaviour, due to these strong reflectors, urban scenes include a high number of high amplitude samples, which implies that urban scenes are mostly heavy-tailed. The proposed Cauchy-Rician model contributes to the literature by leveraging non-zero location (Rician) heavy-tailed (Cauchy) signal components. In the experimental analysis, the Cauchy-Rician model is investigated in comparison to state-of-the-art statistical models that include G0, generalized gamma, and the lognormal distribution. The numerical analysis demonstrates the superior performance and flexibility of the proposed distribution for modelling urban scenes