Numerical Assessment of Alternating Projection Methods for Matrix Completion with Application to Sparse Image Reconstruction

In this paper, we evaluate the numerical performance of the alternating projection method (APM) and a regularized variant of the same method (RAPM) for matrix completion. Both methods are based on the reformulation of matrix completion as a nonconvex feasibility problem. However, the regularized method shares global convergence guarantees even in the nonconvex setting, unlike its standard counterpart. Numerical experiments on randomly generated Gaussian matrices show that RAPM is much more robust with respect to the choice of the initial guess than APM is, as well as being insensitive to the regularization effect for a wide range of regularization parameters. Preliminary numerical results showing the effectiveness of RAPM on some sparse image reconstruction test problems are also presented.