# Space-variant Generalized Gaussian Regularization for Image Restoration

## TL;DR

This paper introduces a space-variant regularizer based on a local half-Generalized Gaussian distribution for image restoration, adaptable to various noise types and image gradient distributions, with automatic parameter estimation.

## Contribution

It proposes a novel, flexible regularizer with per-pixel parameters, coupled with efficient algorithms for high-quality image restoration under different noise conditions.

## Key findings

- Effective in restoring images with diverse gradient distributions.
- Performs well with Gaussian, Laplace, and salt-and-pepper noise.
- Achieves high-quality results in numerical experiments.

## Abstract

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.