Special least squares solutions of the reduced biquaternion matrix equation AX=B with applications.

In this paper, using the real representation method, we study the reduced biquaternion matrix equation A X = B . Taking advantage of the special structure of real representation of reduced biquaternion, we transform the problem of reduced biquaternion matrix into corresponding problem of real matrix. We propose the expressions of the special minimal norm least squares solution of the reduced biquaternion matrix equation A X = B , and the corresponding algorithms only perform real arithmetic. Numerical examples are provided to illustrate that our algorithm are efficient and easily understood. We also apply the minimal norm pure imaginary least squares reduced biquaternion solution to color image restoration. [ABSTRACT FROM AUTHOR]