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Article: Robust quaternion matrix completion with applications to image inpainting

TitleRobust quaternion matrix completion with applications to image inpainting
Authors
Keywordscolor images
convex optimization
low rank
matrix recovery
quaternion
Issue Date2019
Citation
Numerical Linear Algebra with Applications, 2019, v. 26, n. 4, article no. e2245 How to Cite?
Abstract© 2019 John Wiley & Sons, Ltd. In this paper, we study robust quaternion matrix completion and provide a rigorous analysis for provable estimation of quaternion matrix from a random subset of their corrupted entries. In order to generalize the results from real matrix completion to quaternion matrix completion, we derive some new formulas to handle noncommutativity of quaternions. We solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix that is a convex surrogate for the quaternion matrix rank, and the ℓ1-norm of sparse quaternion matrix entries. We show that, under incoherence conditions, a quaternion matrix can be recovered exactly with overwhelming probability, provided that its rank is sufficiently small and that the corrupted entries are sparsely located. The quaternion framework can be used to represent red, green, and blue channels of color images. The results of missing/noisy color image pixels as a robust quaternion matrix completion problem are given to show that the performance of the proposed approach is better than that of the testing methods, including image inpainting methods, the tensor-based completion method, and the quaternion completion method using semidefinite programming.
Persistent Identifierhttp://hdl.handle.net/10722/276521
ISSN
2021 Impact Factor: 2.138
2020 SCImago Journal Rankings: 1.020
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorJia, Zhigang-
dc.contributor.authorNg, Michael K.-
dc.contributor.authorSong, Guang Jing-
dc.date.accessioned2019-09-18T08:33:52Z-
dc.date.available2019-09-18T08:33:52Z-
dc.date.issued2019-
dc.identifier.citationNumerical Linear Algebra with Applications, 2019, v. 26, n. 4, article no. e2245-
dc.identifier.issn1070-5325-
dc.identifier.urihttp://hdl.handle.net/10722/276521-
dc.description.abstract© 2019 John Wiley & Sons, Ltd. In this paper, we study robust quaternion matrix completion and provide a rigorous analysis for provable estimation of quaternion matrix from a random subset of their corrupted entries. In order to generalize the results from real matrix completion to quaternion matrix completion, we derive some new formulas to handle noncommutativity of quaternions. We solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix that is a convex surrogate for the quaternion matrix rank, and the ℓ1-norm of sparse quaternion matrix entries. We show that, under incoherence conditions, a quaternion matrix can be recovered exactly with overwhelming probability, provided that its rank is sufficiently small and that the corrupted entries are sparsely located. The quaternion framework can be used to represent red, green, and blue channels of color images. The results of missing/noisy color image pixels as a robust quaternion matrix completion problem are given to show that the performance of the proposed approach is better than that of the testing methods, including image inpainting methods, the tensor-based completion method, and the quaternion completion method using semidefinite programming.-
dc.languageeng-
dc.relation.ispartofNumerical Linear Algebra with Applications-
dc.subjectcolor images-
dc.subjectconvex optimization-
dc.subjectlow rank-
dc.subjectmatrix recovery-
dc.subjectquaternion-
dc.titleRobust quaternion matrix completion with applications to image inpainting-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1002/nla.2245-
dc.identifier.scopuseid_2-s2.0-85066075394-
dc.identifier.volume26-
dc.identifier.issue4-
dc.identifier.spagearticle no. e2245-
dc.identifier.epagearticle no. e2245-
dc.identifier.eissn1099-1506-
dc.identifier.isiWOS:000474224800004-
dc.identifier.issnl1070-5325-

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