基于低秩正则联合稀疏建模的图像去噪算法  

Low-Rank Regularized Joint Sparsity Modeling for Image Denoising

作　　者：查志远 袁鑫 张嘉超 朱策 ZHA Zhiyuan;YUAN Xin;ZHANG Jiachao;ZHU Ce(College of Communication Engineering,Jilin University,Changchun 130012,China;School of Engineering,Westlake University,Hangzhou 310024,China;Artificial Intelligence Institute of Industrial Technology,Nanjing Institute of Technology,Nanjing 211167,China;School of Information and Communication Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]吉林大学通信工程学院,长春130012 [2]西湖大学工学院,杭州310024 [3]南京工程学院人工智能工业技术研究所,南京211167 [4]电子科技大学信息与通信工程学院,成都611731

出　　处：《电子与信息学报》2025年第2期561-572,共12页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(62471199,62020106011,62271414,61971476,62002160和62072238);吉林大学唐敖庆英才教授启动基金;浙江省杰出青年基金(LR23F010001);西湖基金会(2023GD007)。

摘　　要：非局部稀疏表示模型,如联合稀疏(JS)模型、低秩(LR)模型和组稀疏表示(GSR)模型,通过有效利用图像的非局部自相似(NSS)属性,在图像去噪研究中展现出巨大的潜力。流行的基于字典的JS算法在其目标函数中利用松驰的凸惩罚,避免了NP-hard稀疏编码,但只能得到近似的稀疏表示。这种近似的JS模型未能对潜在的图像数据施加低秩性,从而导致图像去噪质量降低。该文提出一种新颖的低秩正则联合稀疏(LRJS)模型,用于求解图像去噪问题。提出的LRJS模型同时利用非局部相似块的LR和JS先验信息,可以增强非局部相似块之间的相关性(即低秩性),从而可以更好地抑制噪声,提升去噪图像的质量。为了提高优化过程的可处理性和鲁棒性,该文设计了一种具有自适应参数调整策略的交替最小化算法来求解目标函数。在两个图像去噪问题(包括高斯噪声去除和泊松噪声去除)上的实验结果表明,提出的LRJS方法在客观度量和视觉感知上均优于许多现有的流行或先进的图像去噪算法,特别是在处理具有高度自相似性的图像数据时表现更为出色。提出的LRJS图像去噪算法的源代码通过以下链接下载:https://pan.baidu.com/s/14bt6u94NBTZXxhWjBHxn6A?pwd=1234,提取码:1234。Objective Image denoising aims to reduce unwanted noise in images,which has been a long-standing issue in imaging science.Noise significantly degrades image quality,affecting their use in applications such as medical imaging,remote sensing,and image reconstruction.Over recent decades,various image prior models have been developed to address this problem,focusing on different image characteristics.These models,utilizing priors like sparsity,Low-Rankness(LR),and Nonlocal Self-Similarity(NSS),have proven highly effective.Nonlocal sparse representation models,including Joint Sparsity(JS),LR,and Group Sparse Representation(GSR),effectively leverage the NSS property of images.They capture the structural similarity of image patches,even when spatially distant.Popular dictionary-based JS algorithms use a relaxed convex penalty to avoid NP-hard sparse coding,leading to an approximately sparse representation.However,these approximations fail to enforce LR on the image data,reducing denoising quality,especially in cases of complex noise patterns or high self-similarity.This paper proposes a novel Low-Rank Regularized Joint Sparsity(LRJS)model for image denoising,integrating the benefits of LR and JS priors.The LRJS model enhances denoising performance,particularly where traditional methods underperform.By exploiting the NSS in images,the LRJS model better preserves fine details and structures,offering a robust solution for real-world applications.Methods The proposed LRJS model integrates low-rank and JS priors to enhance image denoising performance.By exploiting the NSS property of images,the LRJS model strengthens the dependency between nonlocal similar patches,improving image structure representation and noise suppression.The low-rank prior reflects the smoothness and regularity inherent in the image,whereas the JS prior captures the sparsity of the image patches.Incorporating these priors ensures a more accurate representation of the underlying clean image,enhancing denoising performance.An alternating minimization algo

关 键 词：图像去噪 泊松去噪 非局部稀疏表示 低秩正则联合稀疏 交替最小化算法 自适应参数 

分 类 号：TN911.73[电子电信—通信与信息系统]