Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting
The problem of data reconstruction with partly sampled elements under a tensor structure, which is referred to as tensor completion, is addressed in this paper. The properties of the rank-1 tensor train decomposition and the tensor Kronecker decomposition are introduced at first, and then the tensor...
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| Format: | Article |
| Language: | English |
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IEEE
2018-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8440663/ |
| _version_ | 1818645025844625408 |
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| author | Weize Sun Yuan Chen Hing Cheung So |
| author_facet | Weize Sun Yuan Chen Hing Cheung So |
| author_sort | Weize Sun |
| collection | DOAJ |
| description | The problem of data reconstruction with partly sampled elements under a tensor structure, which is referred to as tensor completion, is addressed in this paper. The properties of the rank-1 tensor train decomposition and the tensor Kronecker decomposition are introduced at first, and then the tensor Kronecker rank as well as Kronecker rank-1 tensor train decomposition are defined. The general tensor completion idea is presented following the criterion of minimizing the number of Kronecker rank-1 tensors, which is relaxed to the thresholding problem and the solution is derived. Furthermore, the number of Kronecker rank-1 tensors that the proposed algorithm can retrieve and its complexity order are analyzed. Computer simulations are carried out on real visual data sets and demonstrate that our method yields a superior performance over the state-of-the-art approaches in terms of recovery accuracy and/or computational complexity. |
| first_indexed | 2024-12-17T00:24:11Z |
| format | Article |
| id | doaj.art-c56055eae1a747bda72b6615f9c58b0f |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-17T00:24:11Z |
| publishDate | 2018-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-c56055eae1a747bda72b6615f9c58b0f2022-12-21T22:10:30ZengIEEEIEEE Access2169-35362018-01-016478044781410.1109/ACCESS.2018.28661948440663Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data InpaintingWeize Sun0Yuan Chen1https://orcid.org/0000-0001-9368-5958Hing Cheung So2Shenzhen University, Shenzhen, ChinaUniversity of Science and Technology Beijing, Beijing, ChinaDepartment of Electronic Engineering, City University of Hong Kong, Hong KongThe problem of data reconstruction with partly sampled elements under a tensor structure, which is referred to as tensor completion, is addressed in this paper. The properties of the rank-1 tensor train decomposition and the tensor Kronecker decomposition are introduced at first, and then the tensor Kronecker rank as well as Kronecker rank-1 tensor train decomposition are defined. The general tensor completion idea is presented following the criterion of minimizing the number of Kronecker rank-1 tensors, which is relaxed to the thresholding problem and the solution is derived. Furthermore, the number of Kronecker rank-1 tensors that the proposed algorithm can retrieve and its complexity order are analyzed. Computer simulations are carried out on real visual data sets and demonstrate that our method yields a superior performance over the state-of-the-art approaches in terms of recovery accuracy and/or computational complexity.https://ieeexplore.ieee.org/document/8440663/Image reconstructionmultidimensional signal processingtensor completiontensor trainKronecker rank-1 decomposition |
| spellingShingle | Weize Sun Yuan Chen Hing Cheung So Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting IEEE Access Image reconstruction multidimensional signal processing tensor completion tensor train Kronecker rank-1 decomposition |
| title | Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting |
| title_full | Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting |
| title_fullStr | Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting |
| title_full_unstemmed | Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting |
| title_short | Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting |
| title_sort | tensor completion using kronecker rank 1 tensor train with application to visual data inpainting |
| topic | Image reconstruction multidimensional signal processing tensor completion tensor train Kronecker rank-1 decomposition |
| url | https://ieeexplore.ieee.org/document/8440663/ |
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