An Alternating Direction Method for Total Variation Denoising

TL;DR

This paper introduces an efficient alternating direction augmented Lagrangian method for total variation image denoising, offering global convergence and competitive performance compared to existing methods.

Contribution

It proposes a novel variable splitting approach for TV denoising that ensures global convergence and improves computational efficiency.

Findings

The method is globally convergent for anisotropic TV.

The method is globally convergent for isotropic TV with additional splitting.

Competitive computational performance demonstrated on standard images.

Abstract

We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an alternating direction augmented Lagrangian (ADAL) method, based on a new variable splitting approach that results in subproblems that can be solved efficiently and exactly. The global convergence of the new algorithm is established for the anisotropic TV model. For the isotropic TV model, by doing further variable splitting, we are able to derive an ADAL method that is globally convergent. We compare our methods with the split Bregman method \cite{goldstein2009split},which is closely related to it, and demonstrate their competitiveness in computational performance on a set of standard test images.