On the use of Gibbs priors for Bayesian image restoration

We propose a new method for selecting both the form of the Gibbs prior potential and the prior parameters used in Bayesian image restoration. The potential is based on specific information about the true image. We focus on pairwise interactions, and we use the probability distribution of the true grey level differences in neighbour pixels to assign the form of the potential. When the distortion is random noise, the distribution of the differences can be estimated directly from the measured image by solving a deconvolution problem. When blur is present, a distribution estimated from one or more similar image(s) without blur can be used. Once the prior has been determined, the parameter of balance between the likelihood and the prior terms of the posterior distribution is selected. This is done by imposing that the information used to build the prior potential is reproduced in the restoration as far as possible. Hence, this provides a fully automatic method. The method is successfully applied to restore both simulated and real Magnetic Resonance (MR) images. (C) 1997 Elsevier Science B.V.