  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.
