  We propose a new space-variant regularization term for variational image
restoration based on the assumption that the gradient magnitudes of the target
image distribute locally according to a half-Generalized Gaussian distribution.
This leads to a highly flexible regularizer characterized by two per-pixel free
parameters, which are automatically estimated from the observed image. The
proposed regularizer is coupled with either the $L_2$ or the $L_1$ fidelity
terms, in order to effectively deal with additive white Gaussian noise or
impulsive noises such as, e.g, additive white Laplace and salt and pepper
noise. The restored image is efficiently computed by means of an iterative
numerical algorithm based on the alternating direction method of multipliers.
Numerical examples indicate that the proposed regularizer holds the potential
for achieving high quality restorations for a wide range of target images
characterized by different gradient distributions and for the different types
of noise considered.
