COLOR IMAGE COMPLETION USING A LOW-RANK QUATERNION MATRIX APPROXIMATION

摘要

In this paper, we propose a lower rank quaternion matrix approximation algorithm and apply it to color image completion. We introduce a concise form for the gradient of a real function in quaternion matrix variables. The optimality conditions of our quaternion least squares problem have a simple expression with this form. The convergence and convergence rate of our algorithm are established with this tool. Numerical tests on a set of color images demonstrate the efficiency of the algorithm.