Generalized Gamma Distribution For Texture Modeling Of Polarimetric SAR Images And Parameter Estimation Using Matrix-Variate Mellin Transform

Polarimetric synthetic aperture radar (Pol.SAR) is a high resolution radar which can obtains the fully polarimetric data, and it’s also characterized by day-or-night, all-weather and high resolution. As we know, the precise modeling of statistical knowledge is a crucial problem in the context of SAR image processing and applications. Up to now, a lot of work related to the statistical nature of single-polarization SAR images has been published in the literature. However, to the best of our knowledge, little attention has been paid to the statistical analysis of multi-polarization SAR data due to its complexity and difficulty.In this paper, we focus on making use of generalized Gamma distribution (GFD) as texture probability density function (PDF) to propose a novel and efficient model for the covariance matrix of multi-look polarimetric SAR data, and present the corresponding parameter estimation based on matrix-variate Mellin transform. The main contents are stated as follows:The core in the modeling of the PolSAR images based on product model is the selection of the texture distribution. To this end, we assume the texture component to be followed GFD which has proved highly flexible and of good fitting, especially including Weibull, Gamma and Inverse Gamma distributions as special cases. As such, we can expect that the resulting model will be not only accurate, but also general to the PolSAR image modeling. This paper proposes the H-Wishart distribution using the GTD) as the texture probability density function which is simplified to a close form containing the Fox-H function by using the Mellin-Barnes integral. In addition, a new multi-texture H-Wishart distribution is derived based on the H-Wishart distribution, which gives the freedom to assume different texture distribution for the co-polarization and cross-polarization.This paper estimates the parameters of the H-Wishart distribution based on the matrix-variable Mellin transform. We get the characteristic function and the corresponding log-cumulant based on the matrix-variable Mellin transform, then use the first three log-cumulant to solve the parameter estimation of the H-Wishart distribution. The goal of the accurate modeling of the PolSAR images has achieved in this paper. The manifolds of theoretical MLCs for several distributions show the intrinsic relationship of the widespread distribution and H-Wishart distribution which can prove the practicability of H-Wishart distribution.