Tensor Completion via Complementary Global, Local, and Nonlocal Priors
Completing missing entries in multidimensional visual data is a typical ill-posed problem that requires appropriate exploitation of prior information of the underlying data. Commonly used priors can be roughly categorized into three classes: global tensor low-rankness, local properties, and nonlocal...
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| Vydané v: | IEEE transactions on image processing Ročník 31; s. 984 - 999 |
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| Hlavní autori: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
United States
IEEE
2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1057-7149, 1941-0042, 1941-0042 |
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| Abstract | Completing missing entries in multidimensional visual data is a typical ill-posed problem that requires appropriate exploitation of prior information of the underlying data. Commonly used priors can be roughly categorized into three classes: global tensor low-rankness, local properties, and nonlocal self-similarity (NSS); most existing works utilize one or two of them to implement completion. Naturally, there arises an interesting question: can one concurrently make use of multiple priors in a unified way, such that they can collaborate with each other to achieve better performance? This work gives a positive answer by formulating a novel tensor completion framework which can simultaneously take advantage of the global-local-nonlocal priors. In the proposed framework, the tensor train (TT) rank is adopted to characterize the global correlation; meanwhile, two Plug-and-Play (PnP) denoisers, including a convolutional neural network (CNN) denoiser and the color block-matching and 3 D filtering (CBM3D) denoiser, are incorporated to preserve local details and exploit NSS, respectively. Then, we design a proximal alternating minimization algorithm to efficiently solve this model under the PnP framework. Under mild conditions, we establish the convergence guarantee of the proposed algorithm. Extensive experiments show that these priors organically benefit from each other to achieve state-of-the-art performance both quantitatively and qualitatively. |
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| AbstractList | Completing missing entries in multidimensional visual data is a typical ill-posed problem that requires appropriate exploitation of prior information of the underlying data. Commonly used priors can be roughly categorized into three classes: global tensor low-rankness, local properties, and nonlocal self-similarity (NSS); most existing works utilize one or two of them to implement completion. Naturally, there arises an interesting question: can one concurrently make use of multiple priors in a unified way, such that they can collaborate with each other to achieve better performance? This work gives a positive answer by formulating a novel tensor completion framework which can simultaneously take advantage of the global-local-nonlocal priors. In the proposed framework, the tensor train (TT) rank is adopted to characterize the global correlation; meanwhile, two Plug-and-Play (PnP) denoisers, including a convolutional neural network (CNN) denoiser and the color block-matching and 3 D filtering (CBM3D) denoiser, are incorporated to preserve local details and exploit NSS, respectively. Then, we design a proximal alternating minimization algorithm to efficiently solve this model under the PnP framework. Under mild conditions, we establish the convergence guarantee of the proposed algorithm. Extensive experiments show that these priors organically benefit from each other to achieve state-of-the-art performance both quantitatively and qualitatively.Completing missing entries in multidimensional visual data is a typical ill-posed problem that requires appropriate exploitation of prior information of the underlying data. Commonly used priors can be roughly categorized into three classes: global tensor low-rankness, local properties, and nonlocal self-similarity (NSS); most existing works utilize one or two of them to implement completion. Naturally, there arises an interesting question: can one concurrently make use of multiple priors in a unified way, such that they can collaborate with each other to achieve better performance? This work gives a positive answer by formulating a novel tensor completion framework which can simultaneously take advantage of the global-local-nonlocal priors. In the proposed framework, the tensor train (TT) rank is adopted to characterize the global correlation; meanwhile, two Plug-and-Play (PnP) denoisers, including a convolutional neural network (CNN) denoiser and the color block-matching and 3 D filtering (CBM3D) denoiser, are incorporated to preserve local details and exploit NSS, respectively. Then, we design a proximal alternating minimization algorithm to efficiently solve this model under the PnP framework. Under mild conditions, we establish the convergence guarantee of the proposed algorithm. Extensive experiments show that these priors organically benefit from each other to achieve state-of-the-art performance both quantitatively and qualitatively. Completing missing entries in multidimensional visual data is a typical ill-posed problem that requires appropriate exploitation of prior information of the underlying data. Commonly used priors can be roughly categorized into three classes: global tensor low-rankness, local properties, and nonlocal self-similarity (NSS); most existing works utilize one or two of them to implement completion. Naturally, there arises an interesting question: can one concurrently make use of multiple priors in a unified way, such that they can collaborate with each other to achieve better performance? This work gives a positive answer by formulating a novel tensor completion framework which can simultaneously take advantage of the global-local-nonlocal priors. In the proposed framework, the tensor train (TT) rank is adopted to characterize the global correlation; meanwhile, two Plug-and-Play (PnP) denoisers, including a convolutional neural network (CNN) denoiser and the color block-matching and 3 D filtering (CBM3D) denoiser, are incorporated to preserve local details and exploit NSS, respectively. Then, we design a proximal alternating minimization algorithm to efficiently solve this model under the PnP framework. Under mild conditions, we establish the convergence guarantee of the proposed algorithm. Extensive experiments show that these priors organically benefit from each other to achieve state-of-the-art performance both quantitatively and qualitatively. |
| Author | Jiang, Tai-Xiang Ng, Michael K. Zhao, Xi-Le Yang, Jing-Hua Ma, Tian-Hui Huang, Ting-Zhu |
| Author_xml | – sequence: 1 givenname: Xi-Le orcidid: 0000-0002-6540-946X surname: Zhao fullname: Zhao, Xi-Le email: xlzhao122003@163.com organization: School of Mathematical Sciences/Research Center for Image and Vision Computing, University of Electronic Science and Technology of China, Chengdu, Sichuan, China – sequence: 2 givenname: Jing-Hua orcidid: 0000-0001-8207-094X surname: Yang fullname: Yang, Jing-Hua email: yangjinghua110@126.com organization: Faculty of Information Technology, Macau University of Science and Technology, Macau, China – sequence: 3 givenname: Tian-Hui orcidid: 0000-0003-2631-9485 surname: Ma fullname: Ma, Tian-Hui email: nkmth0307@126.com organization: School of Science, Civil Aviation University of China, Tianjin, China – sequence: 4 givenname: Tai-Xiang orcidid: 0000-0002-9099-4154 surname: Jiang fullname: Jiang, Tai-Xiang email: taixiangjiang@gmail.com organization: School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu, Sichuan, China – sequence: 5 givenname: Michael K. orcidid: 0000-0001-6833-5227 surname: Ng fullname: Ng, Michael K. email: mng@maths.hku.hk organization: Department of Mathematics, The University of Hong Kong, Hong Kong – sequence: 6 givenname: Ting-Zhu orcidid: 0000-0001-7766-230X surname: Huang fullname: Huang, Ting-Zhu email: tingzhuhuang@126.com organization: School of Mathematical Sciences/Research Center for Image and Vision Computing, University of Electronic Science and Technology of China, Chengdu, Sichuan, China |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/34971534$$D View this record in MEDLINE/PubMed |
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| SubjectTerms | Algorithms alternating direction method of multipliers Artificial neural networks color block-matching and 3 D filtering Color matching convolutional neural network Convolutional neural networks Correlation Hyperspectral imaging Ill posed problems Mathematical analysis Matrix decomposition Minimization plug-and-play proximal alternating minimization Self-similarity Tensor train rank Tensors Visualization |
| Title | Tensor Completion via Complementary Global, Local, and Nonlocal Priors |
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