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- Publisher Website: 10.1137/18M1202311
- Scopus: eid_2-s2.0-85070356154
- WOS: WOS:000473117100019
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Article: A corrected tensor nuclear norm minimization method for noisy low-rank tensor completion
Title | A corrected tensor nuclear norm minimization method for noisy low-rank tensor completion |
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Authors | |
Keywords | Error bound Low-rank tensor recovery Tensor nuclear norm Tensor singular value decomposition Tubal rank |
Issue Date | 2019 |
Citation | SIAM Journal on Imaging Sciences, 2019, v. 12, n. 2, p. 1231-1273 How to Cite? |
Abstract | © 2019 Society for Industrial and Applied Mathematics. In this paper, we study the problem of low-rank tensor recovery from limited sampling with noisy observations for third-order tensors. A tensor nuclear norm method based on a convex relaxation of the tubal rank of a tensor has been used and studied for tensor completion. In this paper, we propose to incorporate a corrected term in the tensor nuclear norm method for tensor completion. Theoretically, we provide a nonasymptotic error bound of the corrected tensor nuclear norm model for low-rank tensor completion. Moreover, we develop and establish the convergence of a symmetric Gauss{Seidel based multiblock alternating direction method of multipliers to solve the proposed correction model. Extensive numerical examples on both synthetic and real-world data are presented to validate the superiority of the proposed model over several state-of-the-art methods. |
Persistent Identifier | http://hdl.handle.net/10722/276652 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Zhang, Xiongjun | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:15Z | - |
dc.date.available | 2019-09-18T08:34:15Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | SIAM Journal on Imaging Sciences, 2019, v. 12, n. 2, p. 1231-1273 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276652 | - |
dc.description.abstract | © 2019 Society for Industrial and Applied Mathematics. In this paper, we study the problem of low-rank tensor recovery from limited sampling with noisy observations for third-order tensors. A tensor nuclear norm method based on a convex relaxation of the tubal rank of a tensor has been used and studied for tensor completion. In this paper, we propose to incorporate a corrected term in the tensor nuclear norm method for tensor completion. Theoretically, we provide a nonasymptotic error bound of the corrected tensor nuclear norm model for low-rank tensor completion. Moreover, we develop and establish the convergence of a symmetric Gauss{Seidel based multiblock alternating direction method of multipliers to solve the proposed correction model. Extensive numerical examples on both synthetic and real-world data are presented to validate the superiority of the proposed model over several state-of-the-art methods. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Imaging Sciences | - |
dc.subject | Error bound | - |
dc.subject | Low-rank tensor recovery | - |
dc.subject | Tensor nuclear norm | - |
dc.subject | Tensor singular value decomposition | - |
dc.subject | Tubal rank | - |
dc.title | A corrected tensor nuclear norm minimization method for noisy low-rank tensor completion | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/18M1202311 | - |
dc.identifier.scopus | eid_2-s2.0-85070356154 | - |
dc.identifier.volume | 12 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 1231 | - |
dc.identifier.epage | 1273 | - |
dc.identifier.eissn | 1936-4954 | - |
dc.identifier.isi | WOS:000473117100019 | - |
dc.identifier.issnl | 1936-4954 | - |