The Split Quaternion Least Squares Problem With Equality Constraint and Its Application

ABSTRACT By applying the real representation matrix and the Moore–Penrose inverse of the split quaternion matrix, we first study the split quaternion least squares problem with equality constraint (SQLSE) and obtain its general solution and minimum norm solution. Then, we obtain the Karush–Kuhn–Tucker equation, which is an equivalent problem of the SQLSE problem. Immediately after, we propose a numerical algorithm on the real number field for the minimum norm solution of the SQLSE problem and enumerate three examples to display its validity. Eventually, we provide an application of the SQLSE problem in the color image restoration.