Enhanced Low-Rank Matrix Approximation
This is an incremental improvement for matrix approximation in tasks like image denoising.
The paper tackles the problem of low-rank matrix approximation by proposing a convex optimization with non-convex regularization to estimate singular values more accurately than the nuclear norm, resulting in a closed-form solution and application to image denoising.
This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero 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 non-convex regularizer) is also derived. The solution reduces to singular value thresholding method as a special case. The proposed method is demonstrated for image denoising.