Adaptive discontinuity location in image restoration

Discontinuity-preserving Bayesian image restoration, based on Markov random fields (MRF), involves an intensity field, representing the image to be restored, and an edge (discontinuity) field. The usual strategy is to perform joint maximum a posteriori (MAP) estimation of the intensity and discontinuity fields, this requiring the specification of Bayesian priors. Departing from this approach, we interpret the discontinuity locations as deterministic unknown parameters of the intensity field. This leads to a parameter estimation problem with the important feature of having an unknown number of parameters. We introduce a discontinuity-preserving image restoration criterion (and an algorithm to implement it) based on the minimum description length (MDL) principle and built upon a compound Gauss-Markov random field (CGMRF) model; the proposed formulation does not involve the specification of a prior for the edge field which is adaptively inferred from the data.