STABLE QUATERNION PRINCIPAL COMPONENT PURSUIT

被引：0

作者：

Li, Wenxin ^{[1
]}

Zhang, Ying ^{[1
]}

机构：

[1] Tianjin Univ, Sch Math, Tianjin 300072, Peoples R China

来源：

PACIFIC JOURNAL OF OPTIMIZATION | 2023年 / 19卷 / 04期

基金：

中国国家自然科学基金;

关键词：

quaternion principal component pursuit; low-rank quaternion matrix; sparse quaternion ma-trix; matrix recovery; MATRICES;

D O I：

暂无

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The relaxed quaternion principal component pursuit is studied to recover low-rank quaternion matrix and sparse quaternion matrix with small entry-wise noise. Stable estimates of the low-rank quaternion matrix and the sparse quaternion matrix are provided by solving a convex minimization problem. The result in this paper generalizes the relaxed principal component pursuit from the case of real matrices to the case of quaternion matrices.

引用

页码：607 / 623

页数：17

共 17 条

[1] Robust Principal Component Analysis? [J].

Candes, Emmanuel J. ;

Li, Xiaodong ;

Ma, Yi ;

Wright, John .

JOURNAL OF THE ACM, 2011, 58 (03)

[2] Exact Matrix Completion via Convex Optimization [J].

Candes, Emmanuel J. ;

Recht, Benjamin .

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2009, 9 (06) :717-772

[3]

Chen YN, 2020, Arxiv, DOI arXiv:2009.12203

[4] Low-Rank Quaternion Approximation for Color Image Processing [J].

Chen, Yongyong ;

Xiao, Xiaolin ;

Zhou, Yicong .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 2020, 29 :1426-1439

[5] Recovering Low-Rank Matrices From Few Coefficients in Any Basis [J].

Gross, David .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (03) :1548-1566

[6]

Hamilton W.R., 1844, Proceedings of the Royal Irish Academy (1836-1869), V3, P1

[7]

Han X, 2013, 2013 6TH INTERNATIONAL CONGRESS ON IMAGE AND SIGNAL PROCESSING (CISP), VOLS 1-3, P358, DOI 10.1109/CISP.2013.6744018

[8] Analysis of a complex of statistical variables into principal components [J].

Hotelling, H .

JOURNAL OF EDUCATIONAL PSYCHOLOGY, 1933, 24 :417-441

[9] Robust quaternion matrix completion with applications to image inpainting [J].

Jia, Zhigang ;

Ng, Michael K. ;

Song, Guang-Jing .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2019, 26 (04)

[10]

Jolliffe Ian T., 1986, Principal component analysis, DOI DOI 10.1016/0169-7439(87)80084-9

← 1 2 →