Least-squares solutions of the reduced biquaternion matrix equation AX=B and their applications in colour image restoration

Abstract

ABSTRACTIn this study, we derive the expressions of the minimal norm least-squares solution for the reduced biquaternion (RB) matrix equation AX=B by using the form of RB matrices, and the Moore–Penrose generalized inverse. Moreover, we investigate their applications in colour image restoration. Therefore, many useful image restoration methods can be extended to reduced biquaternion algebra without separating the colour image into three channels. To prove the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also given.