Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers

TL;DR

This paper introduces a new framework for low-rank tensor completion that uses sparsity-inducing regularizers with closed-form thresholding functions, leading to more efficient algorithms with better performance.

Contribution

The authors propose a novel framework to generate regularizers with closed-form thresholding functions for tensor completion, improving computational efficiency and accuracy.

Findings

Outperforms state-of-the-art methods in synthetic data restoration

Efficient algorithms with proven convergence properties

Effective in real-world tensor completion tasks

Abstract

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.