Matrix Completion Via Reweighted Logarithmic Norm Minimization

• URL: http://arxiv.org/abs/2512.21050v1
• Date: Wed, 24 Dec 2025 08:31:44 GMT
• Title: Matrix Completion Via Reweighted Logarithmic Norm Minimization
• Authors: Zhijie Wang, Liangtian He, Qinghua Zhang, Jifei Miao, Liang-Jian Deng, Jun Liu,
• Abstract summary: The nuclear norm is commonly used as a convex and computationally tractable surrogate for the rank function.<n>We propose a novel reweighted surrogate which provides a closer approximation than many existing alternatives.<n> Experimental results on image inpainting demonstrate that the proposed method superior performance compared to state-of-the-art LRMC approaches.
• Score: 31.786903899545717
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Low-rank matrix completion (LRMC) has demonstrated remarkable success in a wide range of applications. To address the NP-hard nature of the rank minimization problem, the nuclear norm is commonly used as a convex and computationally tractable surrogate for the rank function. However, this approach often yields suboptimal solutions due to the excessive shrinkage of singular values. In this letter, we propose a novel reweighted logarithmic norm as a more effective nonconvex surrogate, which provides a closer approximation than many existing alternatives. We efficiently solve the resulting optimization problem by employing the alternating direction method of multipliers (ADMM). Experimental results on image inpainting demonstrate that the proposed method achieves superior performance compared to state-of-the-art LRMC approaches, both in terms of visual quality and quantitative metrics.

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