From Group Sparse Coding to Rank Minimization: A Novel Denoising Model for Low-level Image Restoration

TL;DR

This paper introduces a novel low-rank minimization denoising model for image restoration that employs a flexible nonconvex rank relaxation and an efficient iterative algorithm, outperforming many existing methods in various IR tasks.

Contribution

It establishes a new connection between group sparse coding and rank minimization, proposing a flexible nonconvex relaxation and an iterative reweighted algorithm for improved image denoising.

Findings

Achieves higher PSNR/FSIM in image IR tasks

Effectively handles compressive sensing, inpainting, deblurring, noise removal

Outperforms several state-of-the-art methods

Abstract

Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with each group contains low-rank property. In this paper, we propose a novel low-rank minimization based denoising model for IR tasks under the perspective of GSC, an important connection between our denoising model and rank minimization problem has been put forward. To overcome the bias problem caused by convex nuclear norm minimization (NNM) for rank approximation, a more generalized and flexible rank relaxation function is employed, namely weighted nonconvex relaxation. Accordingly, an efficient iteratively-reweighted algorithm is proposed to handle the resulting minimization problem combing with the popular L_(1/2) and L_(2/3) thresholding operators. Finally, our proposed denoising model is applied to IR problems via an alternating direction method of multipliers (ADMM) strategy. Typical IR experiments on image compressive sensing (CS), inpainting, deblurring and impulsive noise removal demonstrate that our proposed method can achieve significantly higher PSNR/FSIM values than many relevant state-of-the-art methods.