Document Type

Journal Article

Department/Unit

Department of Computer Science

Language

English

Abstract

In this paper, we study the problem of low-rank tensor recovery from limited sampling with noisy observations for third-order tensors. A tensor nuclear norm method based on a convex relaxation of the tubal rank of a tensor has been used and studied for tensor completion. In this paper, we propose to incorporate a corrected term in the tensor nuclear norm method for tensor completion. Theoretically, we provide a nonasymptotic error bound of the corrected tensor nuclear norm model for low-rank tensor completion. Moreover, we develop and establish the convergence of a symmetric Gauss--Seidel based multiblock alternating direction method of multipliers to solve the proposed correction model. Extensive numerical examples on both synthetic and real-world data are presented to validate the superiority of the proposed model over several state-of-the-art methods.

Keywords

low-rank tensor recovery, tensor nuclear norm, tensor singular value decomposition, tubal rank, error bound

Publication Date

12-2019

Source Publication Title

SIAM Journal on Imaging Sciences

Volume

12

Issue

2

Start Page

1231

End Page

1273

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/18M1202311

Link to Publisher's Edition

https://doi.org/10.1137/18M1202311

ISSN (print)

19364954

Large files may be slow to open. For best results, right-click and select "save as..."

Share

COinS