A new Sylvester-type quaternion matrix equation model for color image data transmission

被引：13

作者：

He, Zhuo-Heng ^{[1
,2
]}

Qin, Wei-Lu ^{[1
,2
]}

Tian, Jie ^{[1
,2
]}

Wang, Xiang-Xiang ^{[3
]}

Zhang, Yang ^{[4
]}

机构：

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

[2] Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China

[3] Univ Nevada, Dept Math & Stat, Reno, NV 89557 USA

[4] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2024年 / 43卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Quaternion; Generalized singular value decomposition; Sylvester equations; Image processing; SINGULAR-VALUE DECOMPOSITION; NEURAL-NETWORK; SKEW FIELD; RESTORATION; AX;

D O I：

10.1007/s40314-024-02732-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate an encryption method for color image data transmission based on Sylvester-type quaternion matrix equations. We first study the solvability conditions and general solution to a system of Sylvester-type quaternion matrix equations. We derive some practical necessary and sufficient conditions for the existence of a solution to this system by using a simultaneous decomposition of quaternion matrices. We present the expression of the general solution to the system when the solvability conditions are satisfied. Based on the form of this system, we consider the applications of this system in color image data transmission. Moreover, we provide some algorithms and examples to illustrate the main results.

引用

页数：30

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