基于稀疏表示和低秩矩阵逼近的图像去噪算法的研究  

Image denoising based on sparse representation and low-rank matrix approximation

作　　者：卢文锋[1] 佀同光[1] 韩国勇 LU Wenfeng;SI Tongguang;HAN Guoyong(School of Management Engineering,Shandong Jianzhu University,Jinan Shandong 250101)

机构地区：[1]山东建筑大学管理工程学院,山东济南250101

出　　处：《首都师范大学学报（自然科学版）》2022年第1期19-23,共5页Journal of Capital Normal University：Natural Science Edition

基　　金：教育部产学合作协同育人项目(202002328023)。

摘　　要：提出了一种基于稀疏表示和低秩矩阵逼近的图像去噪算法:首先,通过对图像块的数据矩阵进行奇异值分解和全局子空间分析,确定信号子空间和噪声子空间;其次,利用图像块与信号子空间的距离寻找相似块,并将相似块分组为训练样本;再次,对相似块矩阵进行奇异值分解,并确定表示相似块的奇异向量;最后,去除表示噪声的基.实验结果表明,该算法能够有效去除图像中的噪声并较好地保留图像细节.This paper proposes an image denoising method based on sparse representation and lowrank matrix approximation. Firstly,it operates the singular value decomposition(SVD)with a data matrix composed of several image patches,and performs the global subspace analysis to define the signal subspace and noise subspace. Secondly,the distance between the image patches and the signal subspace is used to search for similar patches which are grouped into training samples. Thirdly,the singular vectors for representing the corresponding patches can be acquired by operating the SVD on the sample data matrix. Finally,the basis that represents noise is removed. The simulation experiment indicates that it can remove noise efficiently and reserve the image details as much as possible.

关 键 词：稀疏表示 奇异值分解 低秩矩阵逼近 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]