用改进的对数范数提升图像修复质量，效果优于现有方法。
Matrix Completion Via Reweighted Logarithmic Norm Minimization
- 提出加权对数范数作为秩的非凸替代，更贴近真实秩函数。
- 在图像补全任务中，视觉与定量指标均优于当前最优方法。
- 采用ADMM高效求解，适合大规模矩阵补全场景。
低秩矩阵补全（LRMC）在众多应用中表现优异。为应对秩最小化问题的NP难性，通常使用核范数作为秩函数的凸近似，但该方法常因奇异值过度压缩导致次优解。本文提出一种新的加权对数范数作为更优的非凸替代，相比现有方法逼近效果更佳。通过交替方向乘子法（ADMM）高效求解优化问题。在图像修复任务上的实验表明，所提方法在视觉质量与定量指标上均优于当前主流LRMC方法。
原文摘要 · Abstract (English)
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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