First-order phase transit ion and bayesian image processing by loopy belief propagation

The framework is presented of Bayesian image restoration for multi-valued images based on the Q-state Potts model. Hyperparameters in the probabilistic model are determined so as to maximize the marginal likelihood. A practical algorithm is described for multi-valued image restoration based on loopy belief propagation. We conclude that the maximization of marginal likelihood can provide good results even if the a priori probabilistic model exhibits first-order phase transition.