Matrix Completion Via Reweighted Logarithmic Norm Minimization
This work addresses a known bottleneck in matrix completion for applications like image processing, offering incremental improvements over existing methods.
The paper tackled the suboptimal solutions in low-rank matrix completion by proposing a reweighted logarithmic norm as a nonconvex surrogate, achieving superior performance in image inpainting with better visual quality and quantitative metrics compared to state-of-the-art methods.
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.