# Global Weighted Tensor Nuclear Norm for Tensor Robust Principal Component Analysis

arXiv: https://arxiv.org/abs/2209.14084 · HTML: https://mlsanity.com/paper/2209.14084/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 28 Sep 2022.

## Builds on (most cited first, 4 of 4)

- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm](https://mlsanity.com/paper/1712.05870/) (2017)
- [Frequency-Weighted Robust Tensor Principal Component Analysis](https://mlsanity.com/paper/2004.10068/) (2020)
- [T-SVD Based Non-convex Tensor Completion and Robust Principal Component Analysis](https://mlsanity.com/paper/1904.10165/) (2019)

## Abstract (arXiv)

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.