Low-rank tensor completion with a new tensor nuclear norm induced by invertible linear transforms

Lu, C; Peng, X; Wei, Y

Low-rank tensor completion with a new tensor nuclear norm induced by invertible linear transforms

Lu, C Peng, X Wei, Y

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Publisher:: IEEE
Publication Type:: Conference Proceeding
Citation:: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2019, 2019-June, pp. 5989-5997
Issue Date:: 2019-06-01

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Field	Value	Language
dc.contributor.author	Lu, C
dc.contributor.author	Peng, X
dc.contributor.author	Wei, Y
dc.date	2019-06-15
dc.date.accessioned	2020-06-17T19:53:46Z
dc.date.available	2020-06-17T19:53:46Z
dc.date.issued	2019-06-01
dc.identifier.citation	Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2019, 2019-June, pp. 5989-5997
dc.identifier.isbn	9781728132938
dc.identifier.issn	1063-6919
dc.identifier.issn	2575-7075
dc.identifier.uri	http://hdl.handle.net/10453/141497
dc.description.abstract	© 2019 IEEE. This work studies the low-rank tensor completion problem, which aims to exactly recover a low-rank tensor from partially observed entries. Our model is inspired by the recently proposed tensor-tensor product (t-product) based on any invertible linear transforms. When the linear transforms satisfy certain conditions, we deduce the new tensor tubal rank, tensor spectral norm, and tensor nuclear norm. Equipped with the tensor nuclear norm, we then solve the tensor completion problem by solving a convex program and provide the theoretical bound for the exact recovery under certain tensor incoherence conditions. The achieved sampling complexity is order-wise optimal. Our model and result greatly extend existing results in the low-rank matrix and tensor completion. Numerical experiments verify our results and the application on image recovery demonstrates the superiority of our method.
dc.language	en
dc.publisher	IEEE
dc.relation.ispartof	Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
dc.relation.ispartof	IEEE/CVF Conference on Computer Vision and Pattern Recognition
dc.relation.isbasedon	10.1109/CVPR.2019.00615
dc.rights	© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.rights	info:eu-repo/semantics/restrictedAccess
dc.title	Low-rank tensor completion with a new tensor nuclear norm induced by invertible linear transforms
dc.type	Conference Proceeding
utslib.citation.volume	2019-June
utslib.location.activity	Long Beach, CA, USA
utslib.for	0801 Artificial Intelligence and Image Processing
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - CAI - Centre for Artificial Intelligence
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	closed_access	*
pubs.consider-herdc	false
dc.date.updated	2020-06-17T19:53:38Z
pubs.finish-date	2019-06-20
pubs.place-of-publication	Piscataway, USA
pubs.publication-status	Published
pubs.start-date	2019-06-15
pubs.volume	2019-June
dc.location	Piscataway, USA

Abstract:

© 2019 IEEE. This work studies the low-rank tensor completion problem, which aims to exactly recover a low-rank tensor from partially observed entries. Our model is inspired by the recently proposed tensor-tensor product (t-product) based on any invertible linear transforms. When the linear transforms satisfy certain conditions, we deduce the new tensor tubal rank, tensor spectral norm, and tensor nuclear norm. Equipped with the tensor nuclear norm, we then solve the tensor completion problem by solving a convex program and provide the theoretical bound for the exact recovery under certain tensor incoherence conditions. The achieved sampling complexity is order-wise optimal. Our model and result greatly extend existing results in the low-rank matrix and tensor completion. Numerical experiments verify our results and the application on image recovery demonstrates the superiority of our method.

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http://hdl.handle.net/10453/141497