Maximum a posteriori filtering for synthetic aperture radar images based on heavy-tailed Rayleigh distribution of speckle

In order to reflect the statistics of high peak and heavy tail, speckle in synthetic aperture radar images is modeled as heavy-tailed Rayleigh distribution. First, based on Gamma prior distribution and heavy-tailed Rayleigh distribution of speckle, the maximum a posteriori filtering equation is proposed and its analytical form is provided in given characteristic parameter. Second, parameters of heavy-tailed Rayleigh distribution are estimated from the observed image using Mellin transformation. Last, maximum a posteriori de-speckling experiments and their quantitative measures are given. In order to eliminate the influence of window size and noise intensity on de-speckling results, dynamic relations of the de-speckling capability to noise variance and window size are suggested respectively. Results demonstrate that the heavy-tailed Rayleigh distribution accords with the real statistics of speckle, so the maximum a posteriori filter in heavy-tailed Rayleigh distribution of speckle has higher capability of noise reduction compared to the one in Rayleigh distribution of speckle and the Kuan filter.