一种新的广义鲁棒主成分分析模型及其图像去噪应用  

A New Generalized Robust Principal Component Analysis Model and Its Application to Image Denoising

作　　者：袁柳洋[1,2] 汪大为 贾世会 迟晓妮[3] YUAN Liuyang;WANG Dawei;JIA Shihui;CHI Xiaoni(College of Science,Wuhan University of Science and Technology,Wuhan 430081;Hubei Province Key Laboratory of Systems Science in Metallurgical Process,Wuhan 430081;School of Mathematics&Computing Science,Guilin University of Electronic Technology,Guilin 541004)

机构地区：[1]武汉科技大学理学院,武汉430081 [2]武汉科技大学湖北省冶金工业过程系统科学重点实验室,武汉430081 [3]桂林电子科技大学数学与计算科学学院,桂林541004

出　　处：《系统科学与数学》2024年第12期3511-3523,共13页Journal of Systems Science and Mathematical Sciences

基　　金：湖北省教育厅科学技术研究项目(Q20211111);湖北省冶金工业过程系统科学重点实验室开放基金项目(Z202301);国家自然科学基金项目(12361064);广西自然科学基金(2021GXNSFAA220034)资助课题。

摘　　要：文章在结合加权S_p范数最小化的鲁棒主成分分析(WSNM-RPCA)模型与广义鲁棒主成分分析(GRPCA)模型的基础上,同时利用l_(2,1)范数重新构造了一种新的广义鲁棒主成分分析(GWSLRPCA)模型.新的模型提升了对矩阵重要秩成分恢复的准确性,并运用随机排序的交替方向乘子法对新模型进行求解.数值实验结果显示,新的模型GWSLRPCA对被混合噪声污染的图片不仅能分离出图片的有效低秩信息以及其他的噪声部分,而且GWSLRPCA的图像恢复效果更佳.在客观评价标准上GWSLRPCA的各项数据也优于Mean-Filter、WSNM-RPCA与GRPCA模型.In this paper,based on the combination of the robust principal component analysis(WSNM-RPCA)model with weighted norm minimization and the generalized robust principal component analysis(GRPCA)model,a new generalized robust principal component analysis(GWSLRPCA)model is reconstructed by using the l_(2,1)norm,which improves the accuracy of the recovery of the important rank components of the matrix,and uses the alternating direction multiplier method of random ordering to solve the new model.The numerical experiment results show that the new model GWSLRPCA can not only separate the effective low rank information of the picture and other noise parts from the picture polluted by mixed noise,but also have better image restoration effect.In terms of objective evaluation criteria,GWSLRPCA data are also better than Mean-Filter,WSNM-RPCA and GRPCA models.

关 键 词：加权S_(p)范数 l_(2 1)范数 混合噪声 鲁棒性 随机排序 交替方向乘子法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O212.4[自动化与计算机技术—计算机科学与技术]