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
收藏
页码：10 / 20
页数：11
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