A generalized Boltzmann Machine for learning gibbs priors in edge-preserving image restoration

The most successful methods to stabilize inverse ill-posed problems in visual reconstruction are based on the use of a priori information about the local regularity of the image as well as constraints on the geometry of its discontinuities. In the Bayesian approach, using MRF models, prior knowledge is incorporated into the problem via a parametric Gibbs prior and the solution is obtained by minimizing the resulting posterior energy function (MAP estimate). There are two major difficulties with this approach: the non-convexity of the function to be optimized and the choice of the MRF model parameters that best fit the available prior knowledge. Since these parameters considerably affect the quality of the reconstructions, selecting them is a very critical task. This paper deals with the restoration of piecewise smooth images, and proposes a generalized Boltzmann Machine to learn from examples the unknown parameters of the prior model for a given class of images. The trained Boltzmann Machine can then be used in connection with a Hopfield analogue circuit to implement a mixed-annealing scheme for the minimization of the non-convex posterior energy.