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A Fast Algorithm for Cosine Transform Based Tensor Singular Value Decomposition

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arxiv 1902.03070 v1 pith:7DOJYZRS submitted 2019-02-08 cs.CV

Wen-Hao Xu , Xi-Le Zhao , Michael Ng This is my paper · ORCID
classification cs.CV
keywords tensordecompositionsingulartransformvaluecosinematrixblock
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Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on the discrete cosine transform (DCT) matrix. The advantages of using DCT are that (i) the complex arithmetic is not involved in the cosine transform based tensor singular value decomposition, so the computational cost required can be saved; (ii) the intrinsic reflexive boundary condition along the tubes in the third dimension of tensors is employed, so its performance would be better than that by using the periodic boundary condition in DFT. We demonstrate that the tensor product between two tensors by using DCT can be equivalent to the multiplication between a block Toeplitz-plus-Hankel matrix and a block vector. Numerical examples of low-rank tensor completion are further given to illustrate that the efficiency by using DCT is two times faster than that by using DFT and also the errors of video and multispectral image completion by using DCT are smaller than those by using DFT.

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Cited by 3 Pith papers

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