EM algorithm for estimating the parameters of a multivariate complex Rician density for polarimetric SAR

A polarimetric synthetic aperture radar (SAR) forms a complex vector-valued image where each pixel comprises the polarization-dependent reflectivity of a portion of a target or scene. The most common statistical model for this type of image is the zero-mean, circularly-symmetric, multivariate, complex Gaussian model. A logical generalization of this model is a circularly-symmetric, multivariate, complex Rician model which results from having a nonzero-mean complex target reflectivity. Direct maximum-likelihood estimation of the Rician model parameters is infeasible, since setting derivatives equal to zero results in an intractable system of coupled nonlinear equations. The contribution of the paper is a complete iterative solution to the Rician parameter estimation problem by means of the EM (expectation-maximization) algorithm.