Local Bayesian image restoration using variational methods and Gamma-Normal distributions

In this paper we present a new Bayesian methodology for the restoration of blurred and noisy images. Bayesian methods rely on image priors that encapsulate prior image knowledge and avoid the ill-posedness of image restoration problems. We use a spatially varying image prior utilizing a gamma-normal hyperprior distribution on the local precision parameters. This kind of hyperprior distribution, which to our knowledge has not been used before in image restoration, allows for the incorporation of information on local as well as global image variability, models correlation of the local precision parameters and is a conjugate hyperprior to the image model used in the paper. The proposed restoration technique is compared with other image restoration approaches, demonstrating its improved performance.