Monte Carlo Markov Chain techniques for unsupervised MRF-based image denoising

This paper deals with discontinuity-adaptive smoothing for the recovering of degraded images, when MRF models with explicit lines are used, but no a priori information about the free parameters of the related Gibbs distributions is available. The approach adopted is based on the maximization of the posterior distribution with respect to the line field and the Gibbs parameters, while the intensity field is assumed to be clamped to the maximizer of the posterior itself, conditioned on the lines and the parameters. This enables the application of a mixed-annealing algorithm for the MAP estimation of the image field, and of MCMC techniques, over binary variables only, for the simultaneous ML estimation of the parameters. A practical procedure is then derived which is nearly as fast as a single supervised MAP image reconstruction with mixed-annealing. We derive the method for the general case of a linear degradation process plus superposition of additive noise, and experimentally validate it for the sub-case of image denoising.