Variation Methods in Bayesian Image Restoration

Abstract

We present a new approach for parameter estimation in the binary image restoration problem. Within the Bayesian context, we outline the basic conceptual principles of image restoration as well as evaluating some of the more common Monte Carlo techniques such as the Gibbs and Metropolis algorithms, and the much less well known Swendsen-Wang algorithm. We mainly concentrate on two key issues. First, we focus on the quality of restored images with respect to the choice of two restoration parameters that are generally not known. Second, we consider the difficulty in dealing with uncertainty in the restoration parameters. We compute the most likely parameters by maximising the distribution of the noisy image with respect to these parameters. This “evidence” procedure, developed by Gull and MacKay, is a computationally intractable problem. Rather than to resort to uncontrollable Monte Carlo methods to address this issue, we propose to rigorously approximate the evidence by using variational methods which have recently been developed in graphical models problems.