Automatic fidelity and regularization terms selection in variational image restoration

This paper addresses the study of a class of variational models for the image restoration inverse problem. The main assumption is that the additive noise model and the image gradient magnitudes follow a generalized normal (GN) distribution, whose very flexible probability density function (pdf) is characterized by two parameters—typically unknown in real world applications—determining its shape and scale. The unknown image and parameters, which are both modeled as random variables in light of the hierarchical Bayesian perspective adopted here, are jointly automatically estimated within a Maximum A Posteriori (MAP) framework. The hypermodels resulting from the selected prior, likelihood and hyperprior pdfs are minimized by means of an alternating scheme which benefits from a robust initialization based on the noise whiteness property. For the minimization problem with respect to the image, the Alternating Direction Method of Multipliers (ADMM) algorithm, which takes advantage of efficient procedures for the solution of proximal maps, is employed. Computed examples show that the proposed approach holds the potential to automatically detect the noise distribution, and it is also well-suited to process a wide range of images.