Tensor completion via total curvature variation and low-rank matrix factorization

Curvature-based regularization has attracted growing concern in the field of image restoration, benefiting from its favorable geometric properties, such as preserving sharp edges, corners and contrast. Total variation regularization has the ability to promote piecewise smooth property and preserve e...

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Bibliographic Details
Published in:	Applied mathematical modelling Vol. 150; p. 116368
Main Authors:	Xu, Zhi, Yang, Jing-Hua, Zhao, Xi-Le, Yan, Xi-hong, Wang, Chuan-long
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.02.2026
Subjects:	Low-rank matrix factorization Low-rank tensor completion Proximal alternating minimization algorithm Total curvature variation Low-rank matrix factorization Proximal alternating minimization algorithm Total curvature variation Low-rank tensor completion
ISSN:	0307-904X
Online Access:	Get full text
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Summary:	Curvature-based regularization has attracted growing concern in the field of image restoration, benefiting from its favorable geometric properties, such as preserving sharp edges, corners and contrast. Total variation regularization has the ability to promote piecewise smooth property and preserve edges in image processing. Inspired by the advantages of curvature regularization and total variation, in the paper, we first develop a regularization that combines curvature and total variation to explore the geometric characteristics inside high-dimensional data, called total curvature variation (TCV) regularization, which can better preserve local information of the underlying data. We present a new low-rank tensor completion model via TCV and low-rank matrix factorization, which can simultaneously exploits the global low-rank prior and local structure information of data. We solve the proposed minimization problem by using the effective proximal alternating minimization algorithm with guaranteed convergence. Results from experiments on color images, videos, and magnetic resonance images show the superior performance of the proposed method over the compared methods in terms of quantitative and qualitative evaluations. •Design a total curvature variation (TCV) regularization to capture the geometric properties.•Present a LRTC model by incorporating TCV into low-rank matrix factorization.•Employ a proximal alternating minimization (PAM) algorithm to solve the proposed minimization problem.
ISSN:	0307-904X
DOI:	10.1016/j.apm.2025.116368