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

arXiv: https://arxiv.org/abs/1704.01429 · HTML: https://mlsanity.com/paper/1704.01429/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2017.

## Built on by (most cited first, 5 of 5)

- [PoGaIN: Poisson-Gaussian Image Noise Modeling from Paired Samples](https://mlsanity.com/paper/2210.04866/) (2022)
- [Solving Imaging Inverse Problems Using Plug-and-Play Denoisers: Regularization and Optimization Perspectives](https://mlsanity.com/paper/2509.03475/) (2025)
- [Robust Low-Rank Tensor Completion based on M-product with Weighted Correlated Total Variation and Sparse Regularization](https://mlsanity.com/paper/2604.13525/) (2026)
- [Target Aware Poisson-Gaussian Noise Parameters Estimation from Noisy Images](https://mlsanity.com/paper/2210.12142/) (2022)
- [A Novel Truncated Norm Regularization Method for Multi-channel Color Image Denoising](https://mlsanity.com/paper/2307.07932/) (2023)

## Abstract (arXiv)

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 ℓp 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 ℓp 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.