Robust Low-rank Tensor Recovery: Models and Algorithms

11/24/2013
by   Donald Goldfarb, et al.
0

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 of real applications the practical effectiveness of this convex optimization framework for robust low-rank tensor recovery.

READ FULL TEXT

page 15

page 16

page 18

page 19

research
05/06/2023

Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption

We study the tensor robust principal component analysis (TRPCA) problem,...
research
10/17/2021

Fully-Connected Tensor Network Decomposition for Robust Tensor Completion Problem

The robust tensor completion (RTC) problem, which aims to reconstruct a ...
research
02/04/2023

Guaranteed Tensor Recovery Fused Low-rankness and Smoothness

The tensor data recovery task has thus attracted much research attention...
research
09/28/2022

A Parameter-free Nonconvex Low-rank Tensor Completion Model for Spatiotemporal Traffic Data Recovery

Traffic data chronically suffer from missing and corruption, leading to ...
research
01/15/2021

Local Search Algorithms for Rank-Constrained Convex Optimization

We propose greedy and local search algorithms for rank-constrained conve...
research
11/04/2022

Tensor Robust PCA with Nonconvex and Nonlocal Regularization

Tensor robust principal component analysis (TRPCA) is a promising way fo...
research
02/13/2021

Regularized Kaczmarz Algorithms for Tensor Recovery

Tensor recovery has recently arisen in a lot of application fields, such...

Please sign up or login with your details

Forgot password? Click here to reset