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Weidling, Frederic
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Weidling, Frederic
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Weidling, Frederic
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Weidling, F.
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2017Journal Article [["dc.bibliographiccitation.firstpage","598"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","SIAM Journal on Numerical Analysis"],["dc.bibliographiccitation.lastpage","620"],["dc.bibliographiccitation.volume","55"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Weidling, Frederic"],["dc.date.accessioned","2020-12-10T18:37:19Z"],["dc.date.available","2020-12-10T18:37:19Z"],["dc.date.issued","2017"],["dc.description.abstract","We describe a general strategy for the verification of variational source condition by formulating two sufficient criteria describing the smoothness of the solution and the degree of illposedness of the forward operator in terms of a family of subspaces. For linear deterministic inverse problems we show that variational source conditions are necessary and sufficient for convergence rates of spectral regularization methods, which are slower than the square root of the noise level. A similar result is shown for linear inverse problems with white noise. In many cases variational source conditions can be characterized by Besov spaces. This is discussed for a number of prominent inverse problems."],["dc.identifier.doi","10.1137/16M1067445"],["dc.identifier.eissn","1095-7170"],["dc.identifier.gro","3146380"],["dc.identifier.isi","000401780500007"],["dc.identifier.issn","0036-1429"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/76914"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","PUB_WoS_Import"],["dc.publisher","Siam Publications"],["dc.relation.issn","1095-7170"],["dc.relation.issn","0036-1429"],["dc.title","Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]Details DOI WOS2015Journal Article [["dc.bibliographiccitation.artnumber","075006"],["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","7"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.lastpage","14"],["dc.bibliographiccitation.volume","31"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Weidling, Frederic"],["dc.date.accessioned","2017-09-07T11:52:57Z"],["dc.date.available","2017-09-07T11:52:57Z"],["dc.date.issued","2015"],["dc.description.abstract","This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of (logarithmic) rates of convergence for Tikhonov regularization under Sobolev smoothness assumptions for the refractive index. This is achieved by combining two lines of research, conditional stability estimates via geometrical optics solutions and variational regularization theory."],["dc.identifier.doi","10.1088/0266-5611/31/7/075006"],["dc.identifier.gro","3146381"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4151"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Verification of a variational source condition for acoustic inverse medium scattering problems"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]Details DOI2017Journal Article [["dc.bibliographiccitation.firstpage","203"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Inverse Problems and Imaging"],["dc.bibliographiccitation.lastpage","220"],["dc.bibliographiccitation.volume","11"],["dc.contributor.author","Weidling, Frederic"],["dc.contributor.author","Hohage, Thorsten"],["dc.date.accessioned","2017-09-07T11:52:58Z"],["dc.date.available","2017-09-07T11:52:58Z"],["dc.date.issued","2017"],["dc.description.abstract","This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two variational source conditions for near and far field data, which imply logarithmic rates of convergence of regularization methods, in particular Tikhonov regularization, as the noise level tends to 0. Moreover, these variational source conditions imply conditional stability estimates which improve and complement known stability estimates in the literature."],["dc.identifier.doi","10.3934/ipi.2017010"],["dc.identifier.gro","3146398"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4168"],["dc.language.iso","en"],["dc.notes.intern","Not valid abstract: This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a \\\\.fxed frequency. The main results are two variational source conditions for near and far \\\\.feld data, which imply logarithmic rates of convergence of regularization methods, in particular Tikhonov regularization, as the noise level tends to 0. Moreover, these variational source conditions imply conditional stability estimates which improve and complement known stability estimates in the literature."],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]Details DOI2020Book Chapter [["dc.bibliographiccitation.firstpage","145"],["dc.bibliographiccitation.lastpage","164"],["dc.bibliographiccitation.seriesnr","134"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Sprung, Benjamin"],["dc.contributor.author","Weidling, Frederic"],["dc.contributor.editor","Salditt, Tim"],["dc.contributor.editor","Egner, Alexander"],["dc.contributor.editor","Luke, D. Russell"],["dc.date.accessioned","2021-04-21T11:15:35Z"],["dc.date.available","2021-04-21T11:15:35Z"],["dc.date.issued","2020"],["dc.identifier.doi","10.1007/978-3-030-34413-9_5"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/84261"],["dc.relation","SFB 755: Nanoscale Photonic Imaging"],["dc.relation.crisseries","Topics in Applied Physics"],["dc.relation.doi","10.1007/978-3-030-34413-9"],["dc.relation.eisbn","978-3-030-34413-9"],["dc.relation.isbn","978-3-030-34412-2"],["dc.relation.ispartof","Nanoscale Photonic Imaging"],["dc.relation.ispartofseries","Topics in Applied Physics; 134"],["dc.relation.orgunit","Institut für Röntgenphysik"],["dc.subject.gro","SFB 755"],["dc.title","Inverse Problems"],["dc.type","book_chapter"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"],["local.message.claim","2021-12-01T20:54:46.978+0000|||rp114856|||submit_approve|||dc_contributor_author|||None"]]Details DOI