Statistical modeling of polarimetric SAR data: a survey and challenges

Knowledge of the exact statistical properties of the signal plays an important role in the applications of Polarimetric Synthetic Aperture Radar (PolSAR) data. In the last three decades, a considerable research effort has been devoted to finding accurate statistical models for PolSAR data, and a number of distributions have been proposed. In order to see the differences of various models and to make a comparison among them, a survey is provided in this paper. Texture models, which could capture the non-Gaussian behavior observed in high resolution data, and yet keep a compact mathematical form, are mainly explained. Probability density functions for the single look data and the multilook data are reviewed, as well as the advantages and applicable context of those models. As a summary, challenges in the area of statistical analysis of PolSAR data are also discussed.Peer ReviewedPostprint (published version

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

Statistical Modeling of SAR Images: A Survey

Statistical modeling is essential to SAR (Synthetic Aperture Radar) image interpretation. It aims to describe SAR images through statistical methods and reveal the characteristics of these images. Moreover, statistical modeling can provide a technical support for a comprehensive understanding of terrain scattering mechanism, which helps to develop algorithms for effective image interpretation and creditable image simulation. Numerous statistical models have been developed to describe SAR image data, and the purpose of this paper is to categorize and evaluate these models. We first summarize the development history and the current researching state of statistical modeling, then different SAR image models developed from the product model are mainly discussed in detail. Relevant issues are also discussed. Several promising directions for future research are concluded at last

A functional approach to estimation of the parameters of generalized negative binomial and gamma distributions

The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and embraces Poisson distributions, negative binomial distributions, Sichel distributions, Weibull--Poisson distributions and many other types of distributions supplying descriptive statistics with many flexible models. These distributions seem to be very promising for the statistical description of many real phenomena. GG distributions are widely applied in signal and image processing and other practical problems. The statistical estimation of the parameters of GNB and GG distributions is quite complicated. To find estimates, the methods of moments or maximum likelihood can be used as well as two-stage grid EM-algorithms. The paper presents a methodology based on the search for the best distribution using the minimization of $\ell^p$-distances and $L^p$-metrics for GNB and GG distributions, respectively. This approach, first, allows to obtain parameter estimates without using grid methods and solving systems of nonlinear equations and, second, yields not point estimates as the methods of moments or maximum likelihood do, but the estimate for the density function. In other words, within this approach the set of decisions is not a Euclidean space, but a functional space.Comment: 13 pages, 6 figures, The XXI International Conference on Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2018