# Non-Convex Weighted Lp Minimization based Group Sparse Representation Framework for Image Denoising

## TL;DR

This paper introduces a novel non-convex weighted Lp minimization framework for image denoising, utilizing group sparsity and adaptive patch search to outperform existing methods in accuracy and speed.

## Contribution

It proposes a new non-convex weighted Lp minimization approach with a generalized soft-thresholding algorithm and adaptive patch search for improved image denoising.

## Key findings

- Outperforms state-of-the-art methods like BM3D and WNNM.
- Achieves better denoising quality with competitive speed.
- Effectively handles practical image inverse problems.

## Abstract

Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past, convex optimization with sparsity-promoting convex regularization was usually regarded as a standard scheme for estimating sparse signals in noise. However, using convex regularization can not still obtain the correct sparsity solution under some practical problems including image inverse problems. In this paper we propose a non-convex weighted $\ell_p$ minimization based group sparse representation (GSR) framework for image denoising. To make the proposed scheme tractable and robust, the generalized soft-thresholding (GST) algorithm is adopted to solve the non-convex $\ell_p$ minimization problem. In addition, to improve the accuracy of the nonlocal similar patches selection, an adaptive patch search (APS) scheme is proposed. Experimental results have demonstrated that the proposed approach not only outperforms many state-of-the-art denoising methods such as BM3D and WNNM, but also results in a competitive speed.