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

This paper deals with discontinuity-adaptive smoothing for recovering degraded images, when Markov random field models with explicit lines are used, but no a priori information about the free parameters of the related Gibbs distributions is available. The adopted approach 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 maximum a posteriori (MAP) estimation of the image field, and of Markov chain Monte Carlo techniques, over binary variables only, for the simultaneous maximum likelihood estimation of the parameters. A practical procedure is then derived which is nearly as fast as a MAP image reconstruction by mixed-annealing with known Gibbs parameters. 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.

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