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

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.