Tensor Factorization with Total Variation and Tikhonov Regularization for Low-Rank Tensor Completion in Imaging Data
The main aim of this paper is to study tensor factorization for low-rank tensor completion in imaging data. Due to the underlying redundancy of real-world imaging data, the low-tubal-rank tensor factorization (the tensor–tensor product of two factor tensors) can be used to approximate such tensor ve...
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Published in | Journal of mathematical imaging and vision Vol. 62; no. 6-7; pp. 900 - 918 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.07.2020
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | The main aim of this paper is to study tensor factorization for low-rank tensor completion in imaging data. Due to the underlying redundancy of real-world imaging data, the low-tubal-rank tensor factorization (the tensor–tensor product of two factor tensors) can be used to approximate such tensor very well. Motivated by the spatial/temporal smoothness of factor tensors in real-world imaging data, we propose to incorporate a hybrid regularization combining total variation and Tikhonov regularization into low-tubal-rank tensor factorization model for low-rank tensor completion problem. We also develop an efficient proximal alternating minimization (PAM) algorithm to tackle the corresponding minimization problem and establish a global convergence of the PAM algorithm. Numerical results on color images, color videos, and multispectral images are reported to illustrate the superiority of the proposed method over competing methods. |
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ISSN: | 0924-9907 1573-7683 |
DOI: | 10.1007/s10851-019-00933-9 |