Space-variant TV regularization for image restoration

We propose two new variational models aimed to outperform the popular total variation (TV) model for image restoration with L$_2$ and L$_1$ fidelity terms. In particular, we introduce a space-variant generalization of the TV regularizer, referred to as TV$_p^{SV}$, where the so-called shape parameter $p\,$ is automatically and locally estimated by applying a statistical inference technique based on the generalized Gaussian distribution. The restored image is efficiently computed by using an alternating direction method of multipliers procedure. We validated our models on images corrupted by Gaussian blur and two important types of noise, namely the additive white Gaussian noise and the impulsive salt and pepper noise. Numerical examples show that the proposed approach is particularly effective and well suited for images characterized by a wide range of gradient distributions.