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In this paper, we propose a family of non-homogeneous Gauss-Markov elds with Potts region labels model for images to be used in a Bayesian estimation framework, in order to jointly restore and segment images degraded by a known point spread function and additive noise. The joint posterior law of all the unknowns ( the unknown image, its segmentation hidden variable and all the hyperparameters) is approximated by a separable probability laws via the variational Bayes technique. This approximation gives the possibility to obtain practically implemented joint restoration and segmentation algorithm. We will present some preliminary results and comparison with a MCMC Gibbs sampling based algorithm

VARIATIONAL BAYES WITH GAUSS-MARKOV-POTTS PRIOR MODELS FOR JOINT IMAGE RESTORATION AND SEGMENTATION