Computer Science

CLC number: TP751

A Multi-Scale Group Sparse Representation Model with Weighted Log-Sum Penalty for Image Denoising

一种具有加权对数和惩罚的多尺度组稀疏表示的图像去噪模型

School of Microelectronics and Data Science, Anhui University of Technology, Maanshan 243032, Anhui, China (安徽工业大学　微电子与数据科学学院，安徽　马鞍山　243000)

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 28 July 2025

Abstract

In the field of image denoising, the non-local self-similarity (NSS) prior has been widely validated. By exploiting the similar structural details within groups of similar patches to effectively extract redundant information, it significantly improves the accuracy and quality of image restoration. This method can well preserve textures and edges while removing noise. However, NSS-based methods have certain limitations. They usually process patch groups as a whole and neglect the differences among patches within a group. In addition, constructing similar patch groups using NSS is challenging for highly noisy images, suffering from problems such as scarce similar patches and low similarity. To address these issues, this paper proposes an image denoising model with multi-scale group sparse representation based on weighted log-sum penalty. Based on the original-scale image, a multi-scale image sequence is constructed via upsampling and downsampling operations, which not only generates a large number of similar image patches at each individual scale to expand the overall pool of patch candidates, but also excavates structurally correlated similar patches across different scales through a cross-scale patch matching strategy, thus effectively enhancing the inter-patch similarity. Especially for images with high noise intensity, original image patches are severely disturbed by noise, making it difficult to find a sufficient number of highly similar matching patches at a single scale. In contrast, multi-scale construction can weaken the concentrated impact of noise at a single scale, highlight the inherent structural features of the image at other scales, help select more representative similar patch groups, and alleviate the core problems of scarce similar patches and insufficient similarity in high-noise scenarios. Experimental results demonstrate that the proposed MSGSR-Log model outperforms the state-of-the-art methods.

摘要

在图像去噪领域，非局部自相似性(NSS)先验已被广泛验证。它可以通过利用相似块组内的相似结构细节来有效提取冗余信息，显著提高图像恢复的准确性和质量。该方法在去除噪声的同时能够很好地保留纹理和边缘。然而，基于NSS的方法存在一定的局限性。它们通常将块组作为一个整体进行处理，忽略了组内块之间的差异。此外，对于高噪声图像，使用NSS构建相似块组具有挑战性，存在相似块稀少和相似度低等问题。为了解决这些问题，本文提出了一种具有加权对数和惩罚的多尺度组稀疏表示的图像去噪模型，基于原始尺度图像，通过上采样、下采样方式构建多尺度图像序列，不仅在每个尺度上各自生成大量可用于匹配的图像块，扩大了块的整体数量储备，还能通过跨尺度块匹配策略，挖掘不同尺度下具有结构相关性的相似块，有效提升块间的相似度；尤其是对于具有较高噪声强度的图像，原始图像块受噪声干扰严重，单一尺度下难以找到足够多且相似度高的匹配块，而多尺度构建能够弱化噪声在单一尺度上的集中影响，在其他尺度中突出图像的固有结构特征，帮助筛选出更具代表性的相似块组，缓解高噪声场景下相似块稀少、相似度不足的核心难题。实验表明，所提出的MSGSR-Log模型优于现有的方法。