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Performance Guaranteesfor Schatten-p Quasi-Norm Minimization in Recovery of Low-Rank Matrices
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-7926-5081
2015 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 114, 225-230 p.Article in journal (Refereed) Published
Abstract [en]

We address some theoretical guarantees for Schatten-p   quasi-norm minimization (p∈(0,1]p∈(0,1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaranteed by nuclear norm minimization. Secondly, this sufficient condition leads to a theorem proving that all restricted isometry property (RIP) based sufficient conditions for pℓp quasi-norm minimization generalize to Schatten-p quasi-norm minimization. Based on this theorem, we provide a few RIP-based recovery conditions.

Place, publisher, year, edition, pages
2015. Vol. 114, 225-230 p.
National Category
Signal Processing
URN: urn:nbn:se:kth:diva-165467DOI: 10.1016/j.sigpro.2015.02.025ISI: 000353853800022OAI: diva2:808517

QC 20150513

Available from: 2015-04-28 Created: 2015-04-28 Last updated: 2015-06-12Bibliographically approved

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Malek Mohammadi, MohammadrezaSkoglund, Mikael
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