Performance Guaranteesfor Schatten-p Quasi-Norm Minimization in Recovery of Low-Rank Matrices
2015 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 114, 225-230 p.Article in journal (Refereed) Published
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 ℓpℓp 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.
IdentifiersURN: urn:nbn:se:kth:diva-165467DOI: 10.1016/j.sigpro.2015.02.025ISI: 000353853800022OAI: oai:DiVA.org:kth-165467DiVA: diva2:808517
QC 201505132015-04-282015-04-282015-06-12Bibliographically approved