Enhanced Low-Rank Matrix Approximation

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with nonconvex regularization. We employ parameterized nonconvex penalty functions to estimate the nonzero singular values more accurately than the nuclear norm. A closed-form solution for the global optimum of the proposed objective function (sum of data fidelity and the nonconvex regularizer) is also derived. The solution reduces to singular value thresholding method as a special case. The proposed method is demonstrated for image denoising.