Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm

By Canyi Lu, Jiashi Feng, Yudong Chen, Wei David Liu, Zhouchen Lin, Shuicheng Yan. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2018

988 citations recorded by the source corpus.

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product) [14]. Induced by the t-product, we first rigorously deduce the tensor spectral norm, tensor nuclear norm, and tensor average rank, and show that the tensor nuclear norm is the convex envelope of the tensor average rank within the unit ball of the tensor spectral norm. These definitions, their relationships and properties are consistent with matrix cases. Equipped with the new tensor nuclear norm, we then solve the TRPCA problem by solving a convex program and provide the theoretical guarantee for the exact recovery. Our TRPCA model and recovery guarantee include matrix RPCA as a special case. Numerical experiments verify our results, and the applications to image recovery and background modeling problems demonstrate the effectiveness of our method.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/ae1483451dd70769ccbbf199d99cc553daa19852

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Jungang Yang
2. Yang Sun
3. Zhenming Peng
4. Wei An
5. Landan Zhang

In Computer Vision and Pattern Recognition

1. Jungang Yang
2. Yang Sun
3. Zhenming Peng
4. Wei An
5. Landan Zhang

In Signal Processing

1. Zhenming Peng
2. Landan Zhang

Citations in the corpus

• Infrared Dim and Small Target Detection via Multiple Subspace Learning and Spatial-Temporal Patch-Tensor Model (2021, methodology): “…we denote its tensor tubal rank as the number of nonzero singular tubes of S , which can be described as follows: Definition 4 (Tensor Nuclear Norm) [52]: For A = U ∗ S ∗ V ∗ , the tensor nuclear norm of A can be defined as where r = rank t ( A ) , and S ( i , i , 1 ) denotes the entries on the…”
• Infrared Small Target Detection Based on Partial Sum of the Tensor Nuclear Norm (2019, methodology): “efficie t a fast ay to co te t-S is s o i lgorit 1 [52].”