Maximum Likelihood Blind Image Separation Using Nonsymmetrical Half-Plane Markov Random Fields

Abstract

This paper presents a maximum likelihood approach for blindly separating linear instantaneous mixtures of images. The spatial autocorrelation within each image is described using nonsymmetrical half-plane (NSHP) Markov random fields in order to simplify the joint probability density functions of the source images. A first implementation assuming stationary sources is presented. It is then extended to a more realistic nonstationary image model: two approaches, respectively based on blocking and kernel smoothing, are proposed to cope with the nonstationarity of the images. The estimation of the mixing matrix is performed using an iterative equivariant version of the Newton-Raphson algorithm. Moreover, score functions, required for the computation of the updating rule, are approximated at each iteration by parametric polynomial estimators. Results achieved with artificial mixtures of both artificial and real-world images, including an astrophysical application, clearly prove the high performance of our methods, as compared to classical algorithms.