Color image restoration based on reduced biquaternion matrix singular value decomposition

被引：0

作者：

Cai, Xiao-Min ^{[1
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Ke, Yi-Fen ^{[1
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Chen, Lin-Jie ^{[1
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机构：

[1] Fujian Normal Univ, Sch Math & Stat, Fuzhou 350117, Peoples R China

[2] Fujian Normal Univ, Key Lab Analyt Math & Applicat, Minist Educ, Fuzhou 350117, Peoples R China

[3] Fujian Normal Univ, Fujian Prov Key Lab Stat & Artificial Intelligence, Fuzhou 350117, Peoples R China

[4] Fujian Normal Univ, Fujian Key Lab Analyt Math & Applicat FJKLAMA, RChina, Fuzhou 350117, Peoples R China

[5] Fujian Normal Univ, Ctr Appl Math Fujian Prov, FJNU, Fuzhou 350117, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2025年 / 460卷

关键词：

Complex representation; Singular value decomposition; Reduced biquaternion matrix; Color image restoration; EQUATION;

D O I：

10.1016/j.cam.2024.116428

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the singular value decomposition of reduced biquaternion matrix is studied and its expression is obtained based on the complex representation of reduced biquaternion matrix. In addition, the expression of the minimal norm least squares solution for the reduced biquaternion matrix equation is derived by the generalized inverse. The proposed algorithms are very simple and convenient, because they only involve operations on the field of complex numbers. Finally, in order to prove the authenticity of our algorithms, some numerical examples are presented including color image restoration and comparison with existing results.

引用

页数：14

共 27 条

[1] An introduction to commutative quaternions [J].