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Upper bounds on the error of sparse vector and low-rank matrix recovery
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-0355-2663
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
2016 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 120, 249-254 p.Article in journal (Refereed) PublishedText
Abstract [en]

Suppose that a solution x to an underdetermined linear system b=Ax is given. x is approximately sparse meaning that it has a few large components compared to other small entries. However, the total number of nonzero components of x is large enough to violate any condition for the uniqueness of the sparsest solution. On the other hand, if only the dominant components are considered, then it will satisfy the uniqueness conditions. One intuitively expects that x should not be far from the true sparse solution x0. It was already shown that this intuition is the case by providing upper bounds on ||x-x0|| which are functions of the magnitudes of small components of x but independent from x0. In this paper, we tighten one of the available bounds on ||x-x0|| and extend this result to the case that b is perturbed by noise. Additionally, we generalize the upper bounds to the low-rank matrix recovery problem.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 120, 249-254 p.
Keyword [en]
Approximately sparse solutions, Low-rank matrix recovery, Restricted isometry property, Sparse vector recovery
National Category
Computational Mathematics Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-180902DOI: 10.1016/j.sigpro.2015.09.003ISI: 000367754400022ScopusID: 2-s2.0-84944081362OAI: oai:DiVA.org:kth-180902DiVA: diva2:899302
Note

QC 20160201

Available from: 2016-02-01 Created: 2016-01-25 Last updated: 2016-02-24Bibliographically approved

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Malek Mohammadi, MohammadrezaRojas, CristianJansson, Mikael
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