A flexible space-variant anisotropic regularisation for image restoration with automated parameter selection

TL;DR

This paper introduces a flexible space-variant anisotropic regularisation method for image restoration that adaptively models local image geometry and orientation, leading to improved preservation of textures and details.

Contribution

It presents a novel regularisation term based on a bivariate generalized Gaussian distribution, with an automatic parameter estimation method and an efficient ADMM-based numerical solution.

Findings

Significant quality improvements over state-of-the-art methods.

Effective automatic parameter estimation on synthetic and natural images.

Enhanced preservation of textures and details in restored images.

Abstract

We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian distribution. The highly flexible variational structure of the corresponding regulariser 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. For the numerical solution of the corresponding image restoration model, we use an iterative algorithm based on the Alternating Direction Method of Multipliers (ADMM). A suitable preliminary variable splitting together with a novel result in multivariate non-convex proximal calculus yield a very efficient minimisation algorithm. Several numerical results showing significant quality-improvement of the proposed model with respect to some related state-of-the-art competitors are reported, in particular in terms of texture and detail preservation.