Werner, Frank

[["dc.bibliographiccitation.firstpage","341"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","SIAM Journal on Numerical Analysis"],["dc.bibliographiccitation.lastpage","360"],["dc.bibliographiccitation.volume","54"],["dc.contributor.author","König, Claudia"],["dc.contributor.author","Werner, Frank"],["dc.contributor.author","Hohage, Thorsten"],["dc.date.accessioned","2020-12-10T18:37:19Z"],["dc.date.available","2020-12-10T18:37:19Z"],["dc.date.issued","2016"],["dc.identifier.doi","10.1137/15M1022252"],["dc.identifier.eissn","1095-7170"],["dc.identifier.gro","3146387"],["dc.identifier.issn","0036-1429"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/76912"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","32"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Werner, Frank"],["dc.date.accessioned","2017-09-07T11:52:57Z"],["dc.date.available","2017-09-07T11:52:57Z"],["dc.date.issued","2016"],["dc.format.extent","093001:56pp"],["dc.identifier.doi","10.1088/0266-5611/32/9/093001"],["dc.identifier.gro","3146382"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4152"],["dc.notes.status","public"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Inverse Problems with Poisson Data: statistical regularization theory, applications and algorithms"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1203"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","SIAM Journal on Numerical Analysis"],["dc.bibliographiccitation.lastpage","1221"],["dc.bibliographiccitation.volume","52"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Werner, Frank"],["dc.date.accessioned","2017-09-07T11:52:57Z"],["dc.date.available","2017-09-07T11:52:57Z"],["dc.date.issued","2014"],["dc.description.abstract","We study inverse problems $F(f) =g$ with perturbed right-hand side $g^{\\rm obs}$ corrupted by so-called impulsive noise, i.e., noise which is concentrated on a small subset of the domain of definition of $g$. It is well known that Tikhonov-type regularization with an $\\mathbf{L}^1$ data fidelity term yields significantly more accurate results than Tikhonov regularization with classical $\\mathbf{L}^2$ data fidelity terms for this type of noise. The purpose of this paper is to provide a convergence analysis explaining this remarkable difference in accuracy. Our error estimates significantly improve previous error estimates for Tikhonov regularization with $\\mathbf{L}^1$-fidelity term in the case of impulsive noise. We present numerical results which are in good agreement with the predictions of our analysis."],["dc.identifier.doi","10.1137/130932661"],["dc.identifier.gro","3146383"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4153"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Convergence Rates for Inverse Problems with Impulsive Noise"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","127"],["dc.bibliographiccitation.journal","Electronic Transactions on Numerical Analysis"],["dc.bibliographiccitation.lastpage","152"],["dc.bibliographiccitation.volume","57"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Werner, Frank"],["dc.date.accessioned","2022-09-01T09:51:03Z"],["dc.date.available","2022-09-01T09:51:03Z"],["dc.date.issued","2022"],["dc.identifier.doi","10.1553/etna_vol57s127"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/113869"],["dc.language.iso","en"],["dc.notes.intern","DOI-Import GROB-597"],["dc.relation.eissn","1068-9613"],["dc.relation.issn","1068-9613"],["dc.title","Error estimates for variational regularization of inverse problems with general noise models for data and operator"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","745"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Numerische Mathematik"],["dc.bibliographiccitation.lastpage","779"],["dc.bibliographiccitation.volume","123"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Werner, Frank"],["dc.date.accessioned","2017-09-07T11:52:57Z"],["dc.date.available","2017-09-07T11:52:57Z"],["dc.date.issued","2013"],["dc.description.abstract","We study Newton type methods for inverse problems described by nonlinear operator equations F(u)=g in Banach spaces where the Newton equations F′(un;un+1−un)=g−F(un) are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss–Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepskiĭ-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback–Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performance of the proposed method for these problems is illustrated in numerical examples."],["dc.identifier.doi","10.1007/s00211-012-0499-z"],["dc.identifier.gro","3146384"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/10284"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4154"],["dc.language.iso","en"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","final"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.orgunit","Fakultät für Mathematik und Informatik"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.title","Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]