PolSAR Models with Multimodal Intensities

Polarimetric synthetic aperture radar (PolSAR) systems are an important remote sensing tool. Such systems can provide high spacial resolution images, but they are contaminated by an interference pattern called multidimensional speckle. This fact requires that PolSAR images receive specialised treatment; particularly, tailored models which are close to PolSAR physical formation are sought. In this paper, we propose two new matrix models which arise from applying the stochastic summation approach to PolSAR, called compound truncated Poisson complex Wishart (CTPCW) and compound geometric complex Wishart (CGCW) distributions. These models offer the unique ability to express multimodal data. Some of their mathematical properties are derived and discussed— characteristic function and Mellin-kind log-cumulants (MLCs). Moreover, maximum likelihood (ML) estimation procedures via expectation maximisation algorithm for CTPCW and CGCW parameters are furnished as well as MLC-based goodness-of-fit graphical tools. Monte Carlo experiment results indicate ML estimates perform at what is asymptotically expected (small bias and mean square error) even for small sample sizes. Finally, our proposals are employed to describe actual PolSAR images, presenting evidence that they can outperform other well-known distributions, such as WmC, Gm0 , and Km.