# Space-adaptive anisotropic bivariate Laplacian regularization for image restoration

## TL;DR

This paper introduces a space-adaptive anisotropic bivariate Laplacian regularizer for image restoration, improving upon classical Total Variation by modeling local image geometry and orientation with a flexible, statistically grounded variational approach.

## Contribution

It proposes a novel space-variant regularizer based on bivariate Laplacian distributions, with an automatic parameter estimation method and an efficient ADMM-based minimization algorithm.

## Key findings

- Achieves higher quality image restorations compared to classical TV.
- Demonstrates reliable parameter estimation on synthetic and natural images.
- Shows the effectiveness of the proposed model through experimental results.

## Abstract

In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anisotropic extension of the classical isotropic Total Variation (TV) regularizer. The proposed regularizer comes from the statistical assumption that the gradients of the target image distribute locally according to space-variant bivariate Laplacian distributions. The highly flexible variational structure of the corresponding regularizer encodes several free parameters which hold the potential for faithfully modelling the local geometry in the image and describing local orientation preferences. For an automatic estimation of such parameters, we design a robust maximum likelihood approach and report results on its reliability on synthetic data and natural images. A minimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) is presented for the efficient numerical solution of the proposed variational model. Some experimental results are reported which demonstrate the high-quality of restorations achievable by the proposed model, in particular with respect to classical Total Variation regularization.