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The noise collector for sparse recovery in high dimensions

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Métodos Numéricos y Aplicacioneses
dc.affiliation.institutoUC3M. Instituto Universitario sobre Modelización y Simulación en Fluidodinámica, Nanociencia y Matemática Industrial Gregorio Millán Barbanyes
dc.contributor.authorMoscoso, Miguel
dc.contributor.authorNovikov, Alexei
dc.contributor.authorPapanicolaou, George
dc.contributor.authorTsogka, Chrysoula
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.date.accessioned2021-04-26T15:16:40Z
dc.date.available2021-04-26T15:16:40Z
dc.date.issued2020-05-26
dc.description.abstractThe ability to detect sparse signals from noisy, high-dimensional data is a top priority in modern science and engineering. It is well known that a sparse solution of the linear system Alpharho=b0 can be found efficiently with an l1-norm minimization approach if the data are noiseless. However, detection of the signal from data corrupted by noise is still a challenging problem as the solution depends, in general, on a regularization parameter with optimal value that is not easy to choose. We propose an efficient approach that does not require any parameter estimation. We introduce a no-phantom weight tau and the Noise Collector matrix C and solve an augmented system Alpharho+Ceta=b0+e, where e is the noise. We show that the l1-norm minimal solution of this system has zero false discovery rate for any level of noise, with probability that tends to one as the dimension of b0 increases to infinity. We obtain exact support recovery if the noise is not too large and develop a fast Noise Collector algorithm, which makes the computational cost of solving the augmented system comparable with that of the original one. We demonstrate the effectiveness of the method in applications to passive array imaging.en
dc.description.sponsorshipThe work of M.M. was partially supported by Spanish Ministerio de Ciencia e Innovación Grant FIS2016-77892-R. The work of A.N. was partially supported by NSF Grants DMS-1515187 and DMS-1813943. The work of G.P. was partially supported by Air Force Office of Scientific Research (AFOSR) Grant FA9550-18-1-0519. The work of C.T. was partially supported by AFOSR Grants FA9550-17-1-0238 and FA9550-18-1-0519.en
dc.format.extent7es
dc.identifier.bibliographicCitationProceedings of the National Academy of Sciences of th United States of America, 117(21), May 2020, Pp. 11226-11232en
dc.identifier.doihttps://doi.org/10.1073/pnas.1913995117
dc.identifier.issn1091-6490
dc.identifier.issn0027-8424 (online)
dc.identifier.publicationfirstpage11226es
dc.identifier.publicationissue21es
dc.identifier.publicationlastpage11232es
dc.identifier.publicationtitleProceedings of the National Academy of Sciences of th United States of Americaen
dc.identifier.publicationvolume117es
dc.identifier.urihttps://hdl.handle.net/10016/32485
dc.identifier.uxxiAR/0000025745
dc.language.isoenges
dc.publisherNational Academy of Sciencesen
dc.relation.projectIDGobierno de España. FIS2016-77892-Res
dc.rightsThis open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherHigh-dimensional probabilityen
dc.subject.otherConvex geometryen
dc.subject.otherNoisy dataen
dc.subject.otherSparsity-promoting algorithmsen
dc.titleThe noise collector for sparse recovery in high dimensionsen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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