EM ALGORITHM FOR ESTIMATING THE PARAMETERS OF A MULTIVARIATE COMPLEX RICIAN DENSITY FOR POLARIMETRIC - Acoustics, Speech, and Signal Processing, 1995. ICASSP-95., 1995 International Conference on

A polarimetric synthetic aperture radar (SAR) forms a complex vector-valued image where each pixel comprises the polarizationdependent reflectivity of a portion of a target or scene. The most common statistical model for this type of image is the zero-mean, circularlysymmetric, multivariate, complex Gaussian model. A logical generalization of this model is a circularly-symmetric, multivariate, complex Rician model which results from having a nonzem-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 this paper is a complete iterative solution to the Rician parameter estimation problem by means of the EM (expectationmaximization) algorithm. 1. PROBLEM STATEMENT A polarimetric SAR separately transmits horizontally and vertically polarized pulses and the receiver separately measures the horizontally and vertically polarized components of the returns, which after processing yield four complex-valued SAR images: HH, HV, VH, and VV [l]. Reciprocity implies that the VH and HV images should be equal, so the resulting polarimetric SAR image at a particular pixel can be denoted by a three-component complex vector, x. In turn x can be modelled as the three-component complex reflectivity, y, phase-shifted by an amount corresponding to the two-way range between the radar and the resolution cell,