On solutions of the quaternion matrix equation AX = B and their applications in color image restoration

被引：54

作者：

Yuan, Shi-Fang ^{[1
]}

Wang, Qing-Wen ^{[2
]}

Duan, Xue-Feng ^{[3
]}

机构：

[1] Wuyi Univ, Sch Math & Computat Sci, Jiangmen 529020, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[3] Guilin Univ Elect Technol, Coll Math & Computat Sci, Guilin 541004, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 221卷

基金：

上海市自然科学基金;

关键词：

Matrix equation; Least squares solution; Moore-Penrose generalized inverse; Kronecker product; Quaternion matrices; Image restoration; LEAST-NORM; RANKS;

D O I：

10.1016/j.amc.2013.05.069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By using the complex representation of quaternion matrices, and the Moore-Penrose generalized inverse, we derive the expressions of the least squares solution with the least norm, the least squares pure imaginary solution with the least norm, and the least squares real solution with the least norm for the quaternion matrix equation AX = B, respectively. Finally, we discuss their applications in color image restoration. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：10 / 20

页数：11

共 50 条

[1] Special least squares solutions of the quaternion matrix equation AX = B with applications
Zhang, Fengxia
Wei, Musheng
Li, Ying
Zhao, Jianli
APPLIED MATHEMATICS AND COMPUTATION, 2015, 270 : 425 - 433
[2] The Least Square Solutions to the Quaternion Matrix Equation AX=B
薛有才
数学季刊, 1997, (01) : 87 - 90
[3] Least-squares solutions of the reduced biquaternion matrix equation AX=B and their applications in colour image restoration
Kosal, Hidayet Huda
JOURNAL OF MODERN OPTICS, 2019, 66 (18) : 1802 - 1810
[4] The solutions of the quaternion matrix equation AXε + BXδ=0
Dong, Liqiang
Li, Jicheng
LINEAR ALGEBRA AND ITS APPLICATIONS, 2023, 678 : 227 - 267
[5] On solutions to the quaternion matrix equation AX B+CY D = E*
Wang, Qing-Wen
Zhang, Hua-Sheng
Yu, Shao-Wen
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2008, 17 : 343 - 358
[6] The Re—Positive Semidefinite Solution to the Quaternion Matrix Equation AX=B
Lin Chunyan (Dept.of Basic Science
Shandong Finance College
Jinan)Wang Qingwen (Dept.of Math.)Wang Jinping (Shandong Textile School)
昌潍师专学报, 1997, (02) : 4 - 8
[7] The solution of the equation AX = B using commutative elliptic octonion matrix analysis and its applications in colour image restoration
Surekci, Arzu
Gungor, Mehmet Ali
JOURNAL OF MODERN OPTICS, 2024, 71 (16-18) : 626 - 639
[8] ON THE MATRIX EQUATION AX = B WITH APPLICATIONS TO THE GENERATORS OF A CONTROLLABILITY MATRIX
UHLIG, F
LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 85 : 203 - 209
[9] The Solutions to Matrix Equation AX = B with Some Constraints
Dong, Chang-Zhou
Zhang, Yu-Ping
JOURNAL OF APPLIED MATHEMATICS, 2014,
[10] Special least squares solutions of the reduced biquaternion matrix equation AX = B with applications
Ding, Wenxv
Li, Ying
Wang, Dong
COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (08):

← 1 2 3 4 5 →