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dc.contributor.authorZhao, YB
dc.contributor.authorJiang, Houyuan
dc.contributor.authorLuo, ZQ
dc.date.accessioned2018-10-10T17:31:13Z
dc.date.available2018-10-10T17:31:13Z
dc.date.issued2019-02
dc.identifier.issn1526-5471
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/283592
dc.description.abstractAs one of the most plausible convex optimization methods for sparse data reconstruction, l_1-minimization plays a fundamental role in the development of sparse optimization theory. The stability of this method has been addressed in the literature under various assumptions such as the restricted isometry property, null space property, and mutual coherence. In this paper, we propose a unified means to develop the so-called weak stability theory for 1-minimization methods under the condition called the weak range space property of a transposed design matrix, which turns out to be a necessary and sufficient condition for the standard l_1-minimization method to be weakly stable in sparse data reconstruction. The reconstruction error bounds established in this paper are measured by the so-called Robinson’s constant. We also provide a unified weak stability result for standard l_1-minimization under several existing compressed sensing matrix properties. In particular, the weak stability of l_1-minimization under the constant-free range space property of order k of the transposed design matrix is established for the first time in this paper. Different from the existing analysis, we utilize the classic Ho˙man’s lemma concerning the error bound of linear systems as well as Dudley’s theorem concerning the polytope approximation of the unit l_2-ball to show that l_1-minimization is robustly and weakly stable in recovering sparse data from inaccurate measurements.
dc.publisherInstitute for Operations Research and the Management Sciences
dc.titleWeak stability of l_1-minimization methods in sparse data reconstruction
dc.typeArticle
prism.endingPage195
prism.issueIdentifier1
prism.publicationDate2019
prism.publicationNameMathematics of Operations Research
prism.startingPage173
prism.volume44
dc.identifier.doi10.17863/CAM.30954
dcterms.dateAccepted2017-11-06
rioxxterms.versionofrecord10.1287/moor.2017.0919
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2019-02
dc.contributor.orcidJiang, Houyuan [0000-0002-2466-6929]
dc.identifier.eissn1526-5471
rioxxterms.typeJournal Article/Review
cam.issuedOnline2018-09-14
rioxxterms.freetoread.startdate2019-09-14


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