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Article: Almost everywhere injectivity conditions for the matrix recovery problem

TitleAlmost everywhere injectivity conditions for the matrix recovery problem
Authors
Rong, YiWang, YangXu, Zhiqiang
KeywordsCompressed sensing
Determinant variety
Low-rank matrix recovery
Rank minimization
Issue Date2021
Citation
Applied and Computational Harmonic Analysis, 2021, v. 50, p. 386-400 How to Cite?
DOI: http://dx.doi.org/10.1016/j.acha.2019.09.002
AbstractThe aim of matrix recovery is to recover P∈M⊂Fp×q from LA(P)=(Tr(A1TP),Tr(A2TP),…,Tr(ANTP))T with Aj∈Vj⊂Fp×q, which is raised in many areas. In this paper, we build up a framework for almost everywhere matrix recovery which means LA is almost everywhere injectivity on M. We mainly focus on the following question: how many measurements are needed to recover almost all the matrices in M? For the case where both M and Vj are algebraic varieties, we use the tools from algebraic geometry to study the question and present some results to address it under many different settings.
Persistent Identifierhttp://hdl.handle.net/10722/363335
ISSN
1063-5203
2023 Impact Factor: 2.6
2023 SCImago Journal Rankings: 2.231

 

DC FieldValueLanguage
dc.contributor.authorRong, Yi-
dc.contributor.authorWang, Yang-
dc.contributor.authorXu, Zhiqiang-
dc.date.accessioned2025-10-10T07:46:06Z-
dc.date.available2025-10-10T07:46:06Z-
dc.date.issued2021-
dc.identifier.citationApplied and Computational Harmonic Analysis, 2021, v. 50, p. 386-400-
dc.identifier.issn1063-5203-
dc.identifier.urihttp://hdl.handle.net/10722/363335-
dc.description.abstractThe aim of matrix recovery is to recover P∈M⊂F<sup>p×q</sup> from L<inf>A</inf>(P)=(Tr(A<inf>1</inf><sup>T</sup>P),Tr(A<inf>2</inf><sup>T</sup>P),…,Tr(A<inf>N</inf><sup>T</sup>P))<sup>T</sup> with A<inf>j</inf>∈V<inf>j</inf>⊂F<sup>p×q</sup>, which is raised in many areas. In this paper, we build up a framework for almost everywhere matrix recovery which means L<inf>A</inf> is almost everywhere injectivity on M. We mainly focus on the following question: how many measurements are needed to recover almost all the matrices in M? For the case where both M and V<inf>j</inf> are algebraic varieties, we use the tools from algebraic geometry to study the question and present some results to address it under many different settings.-
dc.languageeng-
dc.relation.ispartofApplied and Computational Harmonic Analysis-
dc.subjectCompressed sensing-
dc.subjectDeterminant variety-
dc.subjectLow-rank matrix recovery-
dc.subjectRank minimization-
dc.titleAlmost everywhere injectivity conditions for the matrix recovery problem-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.acha.2019.09.002-
dc.identifier.scopuseid_2-s2.0-85072376530-
dc.identifier.volume50-
dc.identifier.spage386-
dc.identifier.epage400-
dc.identifier.eissn1096-603X-

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