Global Weighted Tensor Nuclear Norm for Tensor Robust Principal Component Analysis

TL;DR

This paper introduces GWTRPCA, a novel tensor robust PCA method that adaptively weights singular values in the Fourier domain to improve low-rank tensor recovery, validated by experiments.

Contribution

The paper proposes the first global weighted TRPCA approach considering intra- and inter-slice singular values, with an adaptive weight learning strategy and an ADMM-based optimization algorithm.

Findings

More accurate low-tubal-rank tensor recovery.

Effective adaptive weight learning via Modified Cauchy Estimator.

Validated on real-world datasets showing improved performance.

Abstract

Tensor Robust Principal Component Analysis (TRPCA), which aims to recover a low-rank tensor corrupted by sparse noise, has attracted much attention in many real applications. This paper develops a new Global Weighted TRPCA method (GWTRPCA), which is the first approach simultaneously considers the significance of intra-frontal slice and inter-frontal slice singular values in the Fourier domain. Exploiting this global information, GWTRPCA penalizes the larger singular values less and assigns smaller weights to them. Hence, our method can recover the low-tubal-rank components more exactly. Moreover, we propose an effective adaptive weight learning strategy by a Modified Cauchy Estimator (MCE) since the weight setting plays a crucial role in the success of GWTRPCA. To implement the GWTRPCA method, we devise an optimization algorithm using an Alternating Direction Method of Multipliers (ADMM) method. Experiments on real-world datasets validate the effectiveness of our proposed method.