Using a generalized Boltzmann Machine 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). Two major difficulties arise in this approach: the first is related to the non-convexity of the function to be optimized; the second is related to the choice of the MRF model parameters that best fit the available prior knowledge. Since these parameters strongly affect the quality of the reconstructions, their selection is a very critical task. In this paper, with application to the restoration of piecewise smooth images, a generalized Boltzmann Machine is proposed to learn from examples the unknown parameters of the prior model for a given class of images. The trained Boltzmann Machine could be used in connection with a Hopfield analogue circuit to implement a mixed-annealing scheme for the efficient minimization of the non-convex posterior energy.