Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains
We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train initialization procedure is proposed specifically for image...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2021
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| Online Access: | https://hdl.handle.net/1721.1/130089 |
| _version_ | 1826204156534194176 |
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| author | Ko, Ching-Yun Batselier, Kim Yu, Wenjian Wong, Ngai |
| author2 | Massachusetts Institute of Technology. Research Laboratory of Electronics |
| author_facet | Massachusetts Institute of Technology. Research Laboratory of Electronics Ko, Ching-Yun Batselier, Kim Yu, Wenjian Wong, Ngai |
| author_sort | Ko, Ching-Yun |
| collection | MIT |
| description | We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train initialization procedure is proposed specifically for image and video completion, which is demonstrated to ensure fast convergence of the completion algorithm. The tensor train framework is also shown to easily accommodate Total Variation and Tikhonov regularization due to their low-rank tensor train representations. Image and video inpainting experiments verify the superiority of the proposed scheme in terms of both speed and scalability, where a speedup of up to 155\times is observed compared to state-of-the-art tensor completion methods at a similar accuracy. Moreover, we demonstrate the proposed scheme is especially advantageous over existing algorithms when only tiny portions (say, 1%) of the to-be-completed images/videos are known. |
| first_indexed | 2024-09-23T12:49:47Z |
| format | Article |
| id | mit-1721.1/130089 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:49:47Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1300892022-10-01T11:23:12Z Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains Ko, Ching-Yun Batselier, Kim Yu, Wenjian Wong, Ngai Massachusetts Institute of Technology. Research Laboratory of Electronics MIT-IBM Watson AI Lab We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train initialization procedure is proposed specifically for image and video completion, which is demonstrated to ensure fast convergence of the completion algorithm. The tensor train framework is also shown to easily accommodate Total Variation and Tikhonov regularization due to their low-rank tensor train representations. Image and video inpainting experiments verify the superiority of the proposed scheme in terms of both speed and scalability, where a speedup of up to 155\times is observed compared to state-of-the-art tensor completion methods at a similar accuracy. Moreover, we demonstrate the proposed scheme is especially advantageous over existing algorithms when only tiny portions (say, 1%) of the to-be-completed images/videos are known. 2021-03-05T12:33:10Z 2021-03-05T12:33:10Z 2015-08 2020-12-07T17:15:30Z Article http://purl.org/eprint/type/JournalArticle 1057-7149 https://hdl.handle.net/1721.1/130089 Ko, Ching-Yun et al. “Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains.” IEEE Transactions on Image Processing, 29 (August 2015) © 2015 The Author(s) en 10.1109/TIP.2020.2995061 IEEE Transactions on Image Processing Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Ko, Ching-Yun Batselier, Kim Yu, Wenjian Wong, Ngai Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains |
| title | Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains |
| title_full | Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains |
| title_fullStr | Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains |
| title_full_unstemmed | Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains |
| title_short | Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains |
| title_sort | fast and accurate tensor completion with total variation regularized tensor trains |
| url | https://hdl.handle.net/1721.1/130089 |
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