Source separation in images via MRFs with variational approximation

The problem of source separation in two dimensions is studied in this paper. The problem is formulated in the Bayesian framework. The sources are modelled as MRFs to accommodate for the spatially correlated structure of the sources, which we exploit for separation in 2D. The difficulty of working analytically with general Gibbs distributions is overcome by using an approximate density. In this work, the Gibbs distribution is modelled by the product of directional Gaussians. The sources are estimated by Maximuma- Posteriori estimation using the approximate density as the prior. At each iteration of the MAP estimation, an annealing schedule is used for approximate density. This annealing schedule aids the algorithm to converge the global extremum. The mixing matrix is found by Maximum Likelihood estimation.