One-bit tensor completion via transformed tensor singular value decomposition

Hou, Jingyao; Zhang, Feng; Wang, Jianjun

doi:10.1016/j.apm.2021.02.032

Cited by 10 publications

(3 citation statements)

References 35 publications

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“…from the definitional expression (19), and by the definition of the variable tubal rank as stated in Definition 5. To show the "furthermore" part, let A 0 and B 0 be the zeropadding counterparts of A and B, respectively, and D be the T-product of A 0 and B 0 , i.e., D := A 0 * B 0 .…”

Section: Appendix C Proof Of Theoremmentioning

confidence: 99%

See 1 more Smart Citation

Variable T-Product and Zero-Padding Tensor Completion with Applications

Yan

Luo

et al. 2023

Preprint

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The T-product method based upon Discrete Fourier Transformation (DFT) has found wide applications in engineering, in particular, in image processing. In this paper, we propose variable T-product, and apply the Zero-Padding Discrete Fourier Transformation (ZDFT), to convert third order tensor problems to the variable Fourier domain. An additional positive integer parameter is introduced, which is greater than the tubal dimension of the third order tensor. When the additional parameter is equal to the tubal dimension, the ZDFT reduces to DFT. Then, we propose a new tensor completion method based on ZDFT and TV regularization, called VTCTF-TV. Extensive numerical experiment results on visual data demonstrate that the superior performance of the proposed method. In addition, the zero-padding is near the size of the original tubal dimension, the resulting tensor completion can be performed much better.

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Section: Appendix C Proof Of Theoremmentioning

confidence: 99%

“…In 2015, Knerfeld, Kilmer and Aeron [17] further extended T-SVD to the so-called transformed T-SVD by replacing the DFT with an arbitrary invertible linear transformation. Since then, transformed T-SVD has attracted attention of many researcheers [18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Variable T-Product and Zero-Padding Tensor Completion with Applications

Yan

Luo

et al. 2023

Preprint

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“…As a higher order generalization of matrix completion, tensor completion has attracted much more attention recently [25], [26], [27], [28], [29], [30]. Compared to matrix rank, there are various definitions for tensor rank, including CAN-DECOMP/PARAFAC (CP) rank [31], Tucker rank [32], TT rank [33], triple rank [34] and tubal rank [35].…”

Section: Introductionmentioning

confidence: 99%

Tensor factorization based method for low rank matrix completion and its application on tensor completion

Yu¹,

Zhang²

2022

Preprint

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Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency. To this end, we first establish the relationship between matrix rank and tensor tubal rank, and then reformulate matrix completion problem as a tensor completion problem. For the reformulated tensor completion problem, we adopt a two-stage strategy based on tensor factorization algorithm. In this way, a matrix completion problem of big size can be solved via some matrix computations of smaller sizes. For a third order tensor completion problem, to fully exploit the low rank structures, we introduce the double tubal rank which combines the tubal rank and the rank of the mode-3 unfolding matrix. For the mode-3 unfolding matrix rank, we follow the idea of matrix completion. Based on this, we establish a novel model and modify the tensor factorization based algorithm for third order tensor completion. Extensive numerical experiments demonstrate that the proposed methods outperform state-of-the-art methods in terms of both accuracy and running time.

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