An Adaptive Correlated Image Prior for Image Restoration Problems

Image restoration is typically defined as an ill-posed problem which has to be regularized to obtain an acceptable solution. In Bayesian interpretation, regularization is equivalent to prior model of the image. An added value of Bayesian point of view is the ability to form a hierarchical model and estimate the hyperparameters of the prior from the data. Many prior models are available, usually based on automatic relevance determination principle applied to the transformed image. However, the transformation (the most common is a differential operator) is assumed to be known. In this letter, we propose to relax this assumption and estimate the image transformation from the data. The resulting algorithm is analytically tractable using the variational Bayes method. Properties of the new prior are demonstrated on the problem of image superresolution.