Robust Low-Rank Tensor Recovery: Models and Algorithms

By Donald Goldfarb, Zhiwei Qin. SIAM Journal on Matrix Analysis and Applications, 2013

432 citations recorded by the source corpus.

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions, and missing values and has a diverse array of applications. In this paper, we study the problem of robust low-rank tensor recovery in a convex optimization framework, drawing upon recent advances in robust principal component analysis and tensor completion. We propose tailored optimization algorithms with global convergence guarantees for solving both the constrained and the Lagrangian formulations of the problem. These algorithms are based on the highly efficient alternating direction augmented Lagrangian and accelerated proximal gradient methods. We also propose a nonconvex model that can often improve the recovery results from the convex models. We investigate the empirical recoverability properties of the convex and nonconvex formulations and compare the computational performance of the algorithms on simulated data. We demonstrate through a number o...

Subfields: Computational Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/81e8556180e4410b77c4cac9844f3547df97a345

How researchers see this paper

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

In Computational Mathematics

1. Jean Kossaifi
2. Shuicheng Yan
3. Maja Pantic
4. Yannis Panagakis
5. Deyu Meng
6. Qi Xie
7. Zhenming Peng
8. Jiashi Feng

In Computational Mechanics

1. Zhenming Peng
2. Landan Zhang
3. Zhouchen Lin
4. Canyi Lu
5. Jiashi Feng
6. Shuicheng Yan
7. Yimian Dai
8. Yiquan Wu

In Computer Vision and Pattern Recognition

1. Jiashi Feng
2. Luc Van Gool
3. Shuicheng Yan
4. Ming-Hsuan Yang
5. Dacheng Tao
6. Yi Yang
7. Chen Change Loy
8. Xiaogang Wang

Citations in the corpus

• Reweighted Infrared Patch-Tensor Model With Both Nonlocal and Local Priors for Single-Frame Small Target Detection (2017, background): “In [34], Goldfarb and Qin proposed the higher order RPCA (robust tensor recovery)”
• TensorLy: Tensor Learning in Python (2016, methodology): “Going forward we will further extend the available decompositions with other state-of-the-art methods such as PARAFAC2, DEDICOM, etc and also include robust tensor decomposition [4, 9].”
• Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery (2018, methodology): “The comparison methods including three state-of-the-art TRPCA methods: RPCA [36], HoRPCA [24] and t-SVD [74].”
• Infrared Small Target Detection Based on Partial Sum of the Tensor Nuclear Norm (2019, methodology): “Nevertheless, the singleton model [43] used in RIPT ay lead to a suboptimal value, since the sum of nuclear norms (SNN) [44] is not the convex envelope of the corresponding sum of ranks [45].”
• Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization (2016, background): “The first one is to recover face images (of the same person) with random noises as that in [8].”