Color image recovery via quaternion matrix completion

In this paper, we present a new method for recovering the color image in a low sample ratio by solving a nuclear norm minimization optimization problem in quaternion number field. This problem is converted to an equivalent semi-definite programming optimization problem, the latter is then solved by solver package based on primal-dual interior point algorithms. Different choices of the measurement matrix including the real sample matrix, complex sample matrix and quaternion sample matrix are used in the experiments to test its effect on the recovered images. Numerical results show that the proposed method achieves good performance.