Volume 31, Issue 6 e2580
RESEARCH ARTICLE

Robust tensor recovery via a nonconvex approach with ket augmentation and auto-weighted strategy

Wenhui Xie

Wenhui Xie

School of Mathematical Sciences, Soochow University, Suzhou, China

Department of Mathematics, Hangzhou Dianzi University, Hangzhou, China

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Chen Ling

Chen Ling

Department of Mathematics, Hangzhou Dianzi University, Hangzhou, China

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Hongjin He

Corresponding Author

Hongjin He

School of Mathematics and Statistics, Ningbo University, Ningbo, China

Correspondence

Hongjin He, School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China.

Email: [email protected]

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Lei-Hong Zhang

Lei-Hong Zhang

School of Mathematical Sciences, Soochow University, Suzhou, China

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First published: 29 July 2024

Abstract

In this article, we introduce a nonconvex tensor recovery approach, which employs the powerful ket augmentation technique to expand a low order tensor into a high-order one so that we can exploit the advantage of tensor train (TT) decomposition tailored for high-order tensors. Moreover, we define a new nonconvex surrogate function to approximate the tensor rank, and develop an auto-weighted mechanism to adjust the weights of the resulting high-order tensor's TT ranks. To make our approach robust, we add two mode-unfolding regularization terms to enhance the model for the purpose of exploring spatio-temporal continuity and self-similarity of the underlying tensors. Also, we propose an implementable algorithm to solve the proposed optimization model in the sense that each subproblem enjoys a closed-form solution. A series of numerical results demonstrate that our approach works well on recovering color images and videos.

CONFLICT OF INTEREST STATEMENT

This study does not have any conflicts to disclose.

DATA AVAILABILITY STATEMENT

Data sharing is not applicable to this article as no new data were created or analyzed in this article.

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