Mimic Capacity Of Fisher And Generalized Gamma Distributions For High-Resolution SAR Image Statistical Modeling

The aim of this paper is to compare the potential of two popular flexible laws, the Fisher distribution and the Generalized Gamma distribution, for the statistical modeling of high-resolution SAR data through an original “mimicking-based” approach. The presented study allows to evaluate the ability of both laws to correctly imitate or “mimic” another reference law, frequently used for modeling the intensity of SAR images and chosen for instance as the $\mathcal {K}$ law or the Weibull, Beta or log-normal laws in this paper. This study uses log-cumulant statistics for parameter estimation of the imitating law and involves quantitative criteria of comparison based on the Kullback–Leibler divergences between the reference law and the Fisher law or the Generalized Gamma law. The mimicking capacities of both distributions are first analyzed for some sets of parameters describing different studied cases, covering a wide set of possible mimicked reference laws. The high modeling potential of both distributions is then illustrated on heterogeneous subscenes from real SAR intensity data. Pragmatical considerations are also taken into account to draw up recommendations about the preferential use of a distribution and to highlight complementarities of both Fisher and Generalized Gamma distributions, along with limitations of the approach.