广义加权鲁棒主成分分析(GWRPCA)的模型与算法

王兴趣, 贾世会, 迟晓妮

系统科学与数学 ›› 2021, Vol. 41 ›› Issue (12) : 3363-3373.

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系统科学与数学 ›› 2021, Vol. 41 ›› Issue (12) : 3363-3373. DOI: 10.12341/jssms20472

广义加权鲁棒主成分分析(GWRPCA)的模型与算法

    王兴趣1,2, 贾世会1,2, 迟晓妮3
作者信息 +

The Model and Algorithm of Generalized Weighted Robust Principal Component Analysis (GWRPCA)

    WANG Xingqu1,2, JIA Shihui1,2, CHI Xiaoni3
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文章历史 +

摘要

文章基于加权鲁棒主成分分析(WRPCA)模型与广义鲁棒主成分分析(GRPCA)模型,构建了广义加权鲁棒主成分分析(GWRPCA)模型,增加了模型的鲁棒性,并运用随机排序的交替方向算法对新模型进行求解.数值实验结果显示,新的模型GWRPCA对混合噪声污染的图片不仅能够有效的分离出低秩部分,稀疏大噪声部分和稠密小噪声部分,而且GWRPCA的图像去噪效果更佳.客观标准上GWRPCA的PSNR值与ERR值也优于WRPCA与GRPCA模型.

Abstract

Based on the weighted robust principal component analysis (WRPCA) model and the generalized robust principal component analysis (GRPCA) model, so as to build the generalized weighted robust principal component analysis (GWRPCA) model, increase the robustness of the model, and apply the alternating direction algorithm of random sorting to solve the new model. The results of numerical experiments show that when the new model GWRPCA processes images with mixed noise pollution, it can not only effectively separate the low-rank part, the sparse large noise part and the dense small noise part, but also has better image denoising effect. PSNR and ERR values of GWRPCA are also better than those of the WRPCA and GRPCA model in objective standards.

关键词

广义加权鲁棒主成分分析(GWRPCA) / 混合噪声 / 鲁棒性 / 随机排序 / 交替方向算法

Key words

Generalized weighted robust principal component analysis (GWRPCA) / mixed noise / robustness / random sequence / alternating direction algorithm

引用本文

导出引用
王兴趣 , 贾世会 , 迟晓妮. 广义加权鲁棒主成分分析(GWRPCA)的模型与算法. 系统科学与数学, 2021, 41(12): 3363-3373. https://doi.org/10.12341/jssms20472
WANG Xingqu , JIA Shihui , CHI Xiaoni. The Model and Algorithm of Generalized Weighted Robust Principal Component Analysis (GWRPCA). Journal of Systems Science and Mathematical Sciences, 2021, 41(12): 3363-3373 https://doi.org/10.12341/jssms20472
中图分类号: 68U10   

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基金

国家自然科学基金(11861026),湖北省冶金工业过程重点实验室(Y201905),广西自然科学基金(2021GXNSFAA220034),湖北省教育厅科学研究计划资助项目青年项目(Q20211111)资助课题.
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