Fast joint separation and segmentation of mixed images

摘要

We consider the problem of the blind separation of noisy instantaneously mixed images. The images are modeled by hidden Markov fields with unknown parameters. Given the observed images, we give a Bayesian formulation and we propose a fast version of the MCMC (Monte Carlo Markov Chain) algorithm based on the Bartlett decomposition for the resulting data augmentation problem. We separate the unknown variables into two categories: 1. The parameters of interest which are the mixing matrix, the noise covari-ance and the parameters of the sources distributions. 2. The hidden variables which are the unobserved sources and the unobserved pixel segmentation 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 great flexibility in the cost function choice. Finally, we show the results for both synthetic and real data to illustrate the feasibility of the proposed solution.