Bayesian Image Restoration Based On Variatonal Inference and a Product of Student-t Priors

Image priors based on products have been recognized to offer many advantages since they provide the ability to enforce simultaneously multiple constraints. However, they are inconvenient for Bayesian inference since their normalization constant cannot be found in closed form. In this paper a new Bayesian framework is proposed for the image restoration problem, where the observed image is degraded by a convolutional operator, which bypasses this difficulty. An image prior is defined by imposing Student-t densities on the outputs of local convolutional filters, which are termed "experts". Thus, this prior can simultaneously smooth flat areas of the image and preserve edges in different directions. The variational methodology is used to fuse the information from all experts and the data in order to infer the restored image. Numerical experiments are shown that demonstrate the advantages of this methodology.