Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high comput...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 33; pp. 2835 - 2850
Main Authors: Qin, Wenjin, Wang, Hailin, Zhang, Feng, Ma, Weijun, Wang, Jianjun, Huang, Tingwen
Format: Journal Article
Language:English
Published: United States IEEE 01.01.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
ADMM algorithm
Algorithms
Approximation
Approximation algorithms
Computational modeling
Computing costs
High-order T-SVD framework
Image reconstruction
Indexes
Mathematical analysis
nonconvex regularizers
Optimization
randomized low-rank tensor approximation
robust high-order tensor completion
Robustness
Singular value decomposition
Tensors
ISSN:1057-7149, 1941-0042, 1941-0042
Online Access:Get full text
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Summary:Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order- d (<inline-formula> <tex-math notation="LaTeX">d\geq 3 </tex-math></inline-formula>) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2024.3385284