Bayesian separation of images modelled with MRFs using MCMC

We investigate the source separation problem of random fields within a Bayesian framework. The Bayesian formulation enables the incorporation of prior image models in the estimation of sources. Due to the intractability of the analytical solution we resort to numerical methods for the joint maximization of the a posteriori distribution of the unknown variables and parameters. We construct the prior densities of pixels using Markov random fields based on a statistical model of the gradient image, and we use a fully Bayesian method with modified-Gibbs sampling. We contrast our work to approximate Bayesian solutions such as Iterated Conditional Modes (ICM) and to non-Bayesian solutions of ICA variety. The performance of the method is tested on synthetic mixtures of texture images and astrophysical images under various noise scenarios. The proposed method is shown to outperform significantly both its approximate Bayesian and non-Bayesian competitors.