Image Restoration using Total Variation with Overlapping Group Sparsity

TL;DR

This paper introduces an overlapping group sparsity total variation regularizer for image restoration, effectively reducing staircase artifacts while preserving edges, and proposes a fast algorithm demonstrating superior performance over existing methods.

Contribution

It proposes a novel overlapping group sparsity TV regularizer and a fast algorithm, improving edge preservation and reducing artifacts in image restoration.

Findings

Outperforms state-of-the-art TV methods in PSNR and error metrics

Reduces staircase artifacts while preserving edges

Demonstrates efficiency and effectiveness in computational experiments

Abstract

Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase-like artifacts. Usually, the high-order total variation (HTV) regularizer is an good option except its over-smoothing property. In this work, we study a minimization problem where the objective includes an usual $l_2$ data-fidelity term and an overlapping group sparsity total variation regularizer which can avoid staircase effect and allow edges preserving in the restored image. We also proposed a fast algorithm for solving the corresponding minimization problem and compare our method with the state-of-the-art TV based methods and HTV based method. The numerical experiments illustrate the efficiency and effectiveness of the proposed method in terms of PSNR, relative error and computing time.