Blind separation of auto-correlated images from noisy mixtures using MRF models

This paper deals with the blind separation and reconstruction of source images from mixtures with unknown coefficients, in presence of noise. We address the blind source separation problem within the ICA approach, i.e. assuming the statistical independence of the sources, and reformulate it in a Bayesian estimation framework. In this way, the flexibility of the Bayesian formulation in accounting for prior knowledge can be exploited to describe correlation within the individual source images, through the use of suitable Gibbs priors. We propose a MAP estimation method and derive a general algorithm for recovering both the mixing matrix and the sources, based on alternating maximization within a simulated annealing scheme. We experimented with this scheme on both synthetic and real images, and found that a source model accounting for correlation is able to increase robustness against noise.