MCMC joint separation and segmentation of hidden Markov fields

Abstract

We consider the problem of the blind separation of noisy instantaneously mixed images. The images are modelized by hidden Markov fields with unknown parameters. Given the observed images, we give a Bayesian formulation and we propose to solve the resulting data augmentation problem by implementing a Monte Carlo Markov chain (MCMC) procedure. We separate the unknown variables into two categories: (1) the parameters of interest which are the mixing matrix, the noise covariance and the parameters of the sources distributions; and (2) the hidden variables which are the unobserved sources and the unobserved pixels classification labels. The proposed algorithm provides in the stationary regime samples drawn from the posterior distributions of all the variables involved in the problem leading to a flexibility in the cost function choice. We discuss and characterize some problems of non-identifiability and degeneracies of the parameters likelihood and the behavior of the MCMC algorithm in this case. Finally, we show the results for both synthetic and real data to illustrate the feasibility of the proposed solution.