Statistical models for SAR amplitude data: A unified vision through Mellin transform and Meijer functions

In the past years, many distributions have been proposed to model SAR images. In previous works, it has been shown that Mellin transform is a powerful tool to analyse random variable products: when speckle is modelled by a Gamma distribution, and when texture can be modelled by a "classical" distribution, Mellin convolution provides analytical expressions of SAR image distribution so that parameter estimations can be processed [13], [11]. In this paper we focus on the product of probability density functions, and more specifically on the Inverse Generalized Gaussian distribution [10]. This approach has been validated in SAR image processing by Frery et al. [7]. We show that the Mellin statistics framework can provide some enlightments about this probability density function family, and can clearly link the Mellin convolution pdf family and the product pdf family. Finally, it will be shown that the Meijer functions give a unified framework for many SAR distributions so that quantitative comparisons between pdf can be achieved.