A Dual Alternating Direction Method of Multipliers for Image Decomposition and Restoration

TL;DR

This paper introduces a dual ADMM algorithm for image decomposition into cartoon and texture components, providing efficient, robust results with higher SNR compared to existing methods.

Contribution

The paper develops a novel dual ADMM algorithm with proven convergence rates for image decomposition and restoration, improving upon existing methods.

Findings

Higher signal-to-noise ratio (SNR) achieved

Algorithm demonstrates efficiency and robustness

Provides convergence analysis under mild conditions

Abstract

In this paper, we develop a dual alternating direction method of multipliers (ADMM) for an image decomposition model. In this model, an image is divided into two meaningful components, i.e., a cartoon part and a texture part. The optimization algorithm that we develop not only gives the cartoon part and the texture part of an image but also gives the restored image (cartoon part + texture part). We also present the global convergence and the local linear convergence rate for the algorithm under some mild conditions. Numerical experiments demonstrate the efficiency and robustness of the dual ADMM (dADMM). Furthermore, we can obtain relatively higher signalto-noise ratio (SNR) comparing to other algorithms. It shows that the choice of the algorithm is also important even for the same model.