Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting

Sun, Weize; Chen, Yuan; So, Hing Cheung

doi:10.1109/access.2018.2866194

Cited by 6 publications

(3 citation statements)

References 35 publications

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“…The

{bold-scriptH}_{p, f_{p}}

, on the other hand, contains the details of the elements in

{bold-scriptX}_{p}^{f_{p}}

. Therefore,

{bold-scriptG}_{p, f_{p}}

is denoted as the ‘background tensor’ and the

{bold-scriptH}_{p, f_{p}}

as ‘detail tensor’ [35].…”

Section: Notations Definitions and Preliminariesmentioning

confidence: 99%

“…Remark According to [35], the (3 r + 1), r = 1, 2, … , R dimensions of

bold-scriptB

that generated from Definition 2.3 contains more detailed information of the original data tensor while the (3 r + 3), r = 0, 1, 2, … , R − 1 dimensions of

bold-scriptB

contains more background information, which is, generally speaking, the adjacent points along the (3 r + 1) dimensions that are more related to each other than the adjacent points along the (3 r + 1) dimensions. Furthermore, we can call the (3 r + 2), r = 1, 2, … , R dimensions of

bold-scriptB

as half detail half background information.…”

Section: Notations Definitions and Preliminariesmentioning

confidence: 99%

“…p . Therefore, G p;f p is denoted as the 'background tensor' and the H p;f p as 'detail tensor'[35]. p ¼ Gunf old 3 P p ðX p Þ ∈ C K p �J p �L p and performing the t-SVD to Z p , we get…”

mentioning

confidence: 99%

See 2 more Smart Citations

Rank revealing‐based tensor completion using improved generalized tensor multi‐rank minimization

Sun

Zhang

Zhao

2021

IET Signal Processing

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The authors address the problem of tensor completion from limited samplings. An improved generalized tubal Kronecker decomposition is first proposed to reveal the tensor structure of the targeted data, and the improved generalized tensor tubal-rank and multi-rank are also introduced. The tensor completion problem is then formulated as the improved multi-rank minimisation problem. Instead of using the singular value decomposition(SVD), this work proposes an alternating optimisation method to update all of the subspaces of the data tensor for the recovery process, and thus it is computationally inexpensive. A rank-decreasing method is derived to reveal the tensor rank in order to avoid the troublesome user defined hyper-parameter selection. Experiments are carried out on both the synthetic data and the real datasets, and it is shown that the proposed approach can get a better performance than the state-of-the-art approaches with moderate computational complexity.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…The

{bold-scriptH}_{p, f_{p}}

, on the other hand, contains the details of the elements in

{bold-scriptX}_{p}^{f_{p}}

. Therefore,

{bold-scriptG}_{p, f_{p}}

is denoted as the ‘background tensor’ and the

{bold-scriptH}_{p, f_{p}}

as ‘detail tensor’ [35].…”

Section: Notations Definitions and Preliminariesmentioning

confidence: 99%

“…Remark According to [35], the (3 r + 1), r = 1, 2, … , R dimensions of

bold-scriptB

that generated from Definition 2.3 contains more detailed information of the original data tensor while the (3 r + 3), r = 0, 1, 2, … , R − 1 dimensions of