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Convergence rates in ℓ¹-regularization when the basis is not smooth enough

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dc.contributor.authorFlemming, Jens
dc.contributor.authorHegland, Markus
dc.date.accessioned2015-03-30T00:41:29Z
dc.date.available2015-03-30T00:41:29Z
dc.date.issued2014-02-26
dc.date.updated2015-12-10T10:00:13Z
dc.description.abstractSparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation with respect to a fixed basis. We drop this sparsity assumption and provide error estimates for nonsparse solutions. After discussing a result in this direction published earlier by one of the authors and co-authors, we prove a similar error estimate under weaker assumptions. Two examples illustrate that this set of weaker assumptions indeed covers additional situations which appear in applications.
dc.description.sponsorshipJ. Flemming was supported by the German Science Foundation (DFG) under grant FL 832/1-1. M. Hegland was partially supported by the Technische Universität München Institute of Advanced Study, funded by the German Excellence Initiative. Work on this article was partially conducted during a stay of M. Hegland at TU Chemnitz, supported by the German Science Foundation (DFG) under grant HO 1454/8-1.en_AU
dc.identifier.issn0003-6811en_AU
dc.identifier.urihttp://hdl.handle.net/1885/13076
dc.publisherTaylor & Francis
dc.rightshttp://www.sherpa.ac.uk/romeo/issn/0003-6811/..."Pre-print or post-print allowed on institutional repository or subject-based repository after either 12 months embargo. On a non-profit server" from SHERPA/RoMEO site (as at 30/03/15)
dc.sourceApplicable Analysis
dc.subjectlinear ill-posed problems
dc.subjectTikhonov-type regularization
dc.subjectℓ1-regularization
dc.subjectnonsmooth basis
dc.subjectsparsity constraints
dc.subjectconvergence rates
dc.subjectvariational inequalities
dc.titleConvergence rates in ℓ¹-regularization when the basis is not smooth enough
dc.typeJournal article
dcterms.dateAccepted2014-01-16
local.bibliographicCitation.issue3en_AU
local.bibliographicCitation.lastpage476en_AU
local.bibliographicCitation.startpage464en_AU
local.contributor.affiliationHegland, M., Mathematical Sciences Institute, The Australian National Universityen_AU
local.contributor.authoruidu9200256en_AU
local.identifier.absfor010200 - APPLIED MATHEMATICS
local.identifier.ariespublicationa383154xPUB1084
local.identifier.citationvolume94en_AU
local.identifier.doi10.1080/00036811.2014.886106en_AU
local.identifier.scopusID2-s2.0-84922431520
local.publisher.urlhttp://www.routledge.com/en_AU
local.type.statusSubmitted Versionen_AU

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