A new image restoration model associated with special elliptic quaternionic least-squares solutions based on LabVIEW

Abstract

In this paper, we take advantage of the elliptic complex matrix representation of elliptic quaternion matrices. Then we obtain the methods of the elliptic quaternionic least-squares solution, the pure elliptic quaternionic least-squares solution, and the real least-squares solution with the least norm of the elliptic quaternion matrix equation AX=B. We also apply the newly obtained method of the pure elliptic quaternionic least-squares solution with the least norm to the color image restoration based on the LabVIEW program. In this context, we propose a new image restoration model called “ELSI image restoration model” associated with elliptic quaternionic least-squares solutions.