Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation
Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high comput...
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| Veröffentlicht in: | IEEE transactions on image processing Jg. 33; S. 2835 - 2850 |
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United States
IEEE
01.01.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order- d (<inline-formula> <tex-math notation="LaTeX">d\geq 3 </tex-math></inline-formula>) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision. |
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| AbstractList | Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order- d ([Formula Omitted]) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision. Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order-d (d ≥ 3) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision. Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order-d ( d ≥ 3 ) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision.Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order-d ( d ≥ 3 ) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision. Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order- d (<inline-formula> <tex-math notation="LaTeX">d\geq 3 </tex-math></inline-formula>) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision. |
| Author | Huang, Tingwen Wang, Jianjun Wang, Hailin Ma, Weijun Qin, Wenjin Zhang, Feng |
| Author_xml | – sequence: 1 givenname: Wenjin orcidid: 0000-0002-8064-4206 surname: Qin fullname: Qin, Wenjin email: qinwenjin2021@163.com organization: School of Mathematics and Statistics, Southwest University, Chongqing, China – sequence: 2 givenname: Hailin orcidid: 0000-0002-7797-2719 surname: Wang fullname: Wang, Hailin email: wanghailin97@163.com organization: School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China – sequence: 3 givenname: Feng orcidid: 0000-0003-1000-8877 surname: Zhang fullname: Zhang, Feng email: zfmath@swu.edu.cn organization: School of Mathematics and Statistics, Southwest University, Chongqing, China – sequence: 4 givenname: Weijun orcidid: 0000-0003-1949-4541 surname: Ma fullname: Ma, Weijun email: Weijunma_2008@sina.com organization: School of Information Engineering, Ningxia University, Yinchuan, China – sequence: 5 givenname: Jianjun orcidid: 0000-0002-5344-4460 surname: Wang fullname: Wang, Jianjun email: wjj@swu.edu.cn organization: School of Mathematics and Statistics, Research Institute of Intelligent Finance and Digital Economics, Southwest University, Chongqing, China – sequence: 6 givenname: Tingwen orcidid: 0000-0001-9610-846X surname: Huang fullname: Huang, Tingwen email: tingwen.huang@qatar.tamu.edu organization: Department of Mathematics, Texas A&M University at Qatar, Doha, Qatar |
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| SubjectTerms | ADMM algorithm Algorithms Approximation Approximation algorithms Computational modeling Computing costs High-order T-SVD framework Image reconstruction Indexes Mathematical analysis nonconvex regularizers Optimization randomized low-rank tensor approximation robust high-order tensor completion Robustness Singular value decomposition Tensors |
| Title | Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation |
| URI | https://ieeexplore.ieee.org/document/10496551 https://www.ncbi.nlm.nih.gov/pubmed/38598373 https://www.proquest.com/docview/3040055593 https://www.proquest.com/docview/3037396620 |
| Volume | 33 |
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