Robust tensor completion using transformed tensor singular value decomposition

Summary In this article, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2020-05, Vol.27 (3), p.n/a
Main Authors: Song, Guangjing, Ng, Michael K., Zhang, Xiongjun
Format: Article
Language:English
Subjects:
Fourier transforms
low‐rank
Mathematical analysis
robust tensor completion
Robustness
Singular value decomposition
sparsity
Tensors
transformed tensor singular value decomposition
unitary transform matrix
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Summary:Summary In this article, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by using other unitary transform matrices than that by using discrete Fourier transform matrix. This would be more effective for robust tensor completion. Experimental results for hyperspectral, video and face datasets have shown that the recovery performance for the robust tensor completion problem by using transformed tensor SVD is better in peak signal‐to‐noise ratio than that by using Fourier transform and other robust tensor completion methods.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2299