Enhanced Low-Rank Matrix Approximation

TL;DR

This paper introduces a novel convex optimization approach with non-convex regularization for more accurate low-rank matrix estimation, providing a closed-form solution and demonstrating effectiveness in image denoising.

Contribution

It presents a new method combining non-convex penalties with convex optimization for improved low-rank matrix approximation, including a closed-form solution.

Findings

More accurate estimation of non-zero singular values.

Closed-form solution derived for the optimization problem.

Effective application demonstrated in image denoising.

Abstract

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.