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","283"],["dc.bibliographiccitation.lastpage","312"],["dc.bibliographiccitation.volume","134"],["dc.contributor.author","Munk, Axel"],["dc.contributor.author","Proksch, Katharina"],["dc.contributor.author","Li, Housen"],["dc.contributor.author","Werner, Frank"],["dc.contributor.editor","Salditt, Tim"],["dc.contributor.editor","Egner, Alexander"],["dc.contributor.editor","Luke, D. Russell"],["dc.date.accessioned","2021-03-05T08:58:56Z"],["dc.date.available","2021-03-05T08:58:56Z"],["dc.date.issued","2020"],["dc.identifier.doi","10.1007/978-3-030-34413-9_11"],["dc.identifier.eisbn","978-3-030-34413-9"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/80304"],["dc.notes.intern","DOI Import GROB-393"],["dc.publisher","Springer International Publishing"],["dc.publisher.place","Cham"],["dc.relation.eissn","1437-0859"],["dc.relation.isbn","978-3-030-34412-2"],["dc.relation.ispartof","Nanoscale Photonic Imaging"],["dc.relation.issn","0303-4216"],["dc.title","Photonic Imaging with Statistical Guarantees: From Multiscale Testing to Multiscale Estimation"],["dc.type","book_chapter"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","3303"],["dc.bibliographiccitation.issue","16"],["dc.bibliographiccitation.journal","Biophysical Journal"],["dc.bibliographiccitation.lastpage","3314"],["dc.bibliographiccitation.volume","120"],["dc.contributor.author","Siegmund, René"],["dc.contributor.author","Werner, Frank"],["dc.contributor.author","Jakobs, Stefan"],["dc.contributor.author","Geisler, Claudia"],["dc.contributor.author","Egner, Alexander"],["dc.date.accessioned","2021-10-01T09:57:28Z"],["dc.date.available","2021-10-01T09:57:28Z"],["dc.date.issued","2021"],["dc.identifier.doi","10.1016/j.bpj.2021.05.031"],["dc.identifier.pii","S0006349521005567"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/89845"],["dc.identifier.url","https://mbexc.uni-goettingen.de/literature/publications/322"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-469"],["dc.relation","EXC 2067: Multiscale Bioimaging"],["dc.relation.issn","0006-3495"],["dc.relation.workinggroup","RG Egner"],["dc.relation.workinggroup","RG Jakobs (Structure and Dynamics of Mitochondria)"],["dc.title","isoSTED microscopy with water-immersion lenses and background reduction"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.subtype","original_ja"],["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","015004"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","36"],["dc.contributor.author","Werner, Frank"],["dc.contributor.author","Hofmann, Bernd"],["dc.date.accessioned","2021-04-14T08:27:32Z"],["dc.date.available","2021-04-14T08:27:32Z"],["dc.date.issued","2019"],["dc.identifier.doi","10.1088/1361-6420/ab4cd7"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/82325"],["dc.notes.intern","DOI Import GROB-399"],["dc.relation.eissn","1361-6420"],["dc.relation.issn","0266-5611"],["dc.title","Convergence analysis of (statistical) inverse problems under conditional stability estimates"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1266"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Bernoulli"],["dc.bibliographiccitation.lastpage","1306"],["dc.bibliographiccitation.volume","24"],["dc.contributor.author","Enikeeva, Farida"],["dc.contributor.author","Munk, Axel"],["dc.contributor.author","Werner, Frank"],["dc.date.accessioned","2020-12-10T18:43:58Z"],["dc.date.available","2020-12-10T18:43:58Z"],["dc.date.issued","2018"],["dc.description.abstract","We analyze the effect of a heterogeneous variance on bump detection in a Gaussian regression model. To this end we allow for a simultaneous bump in the variance and specify its impact on the difficulty to detect the null signal against a single bump with known signal strength. This is done by calculating lower and upper bounds, both based on the likelihood ratio. Lower and upper bounds together lead to explicit characterizations of the detection boundary in several subregimes depending on the asymptotic behavior of the bump heights in mean and variance. In particular, we explicitly identify those regimes, where the additional information about a simultaneous bump in variance eases the detection problem for the signal. This effect is made explicit in the constant and / or the rate, appearing in the detection boundary. We also discuss the case of an unknown bump height and provide an adaptive test and some upper bounds in that case."],["dc.identifier.arxiv","1504.07390"],["dc.identifier.doi","10.3150/16-BEJ899"],["dc.identifier.gro","3145907"],["dc.identifier.issn","1350-7265"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/78283"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1350-7265"],["dc.subject","minimax testing theory heterogeneous Gaussian regression change point detection"],["dc.title","Bump detection in heterogeneous Gaussian regression"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","405"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Annales de l´Institut Henri Poincaré. B, Probability and Statistics"],["dc.bibliographiccitation.lastpage","427"],["dc.bibliographiccitation.volume","56"],["dc.contributor.author","Li, Housen"],["dc.contributor.author","Werner, Frank"],["dc.date.accessioned","2020-12-10T18:41:49Z"],["dc.date.available","2020-12-10T18:41:49Z"],["dc.date.issued","2020"],["dc.identifier.doi","10.1214/19-AIHP966"],["dc.identifier.issn","0246-0203"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/77687"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.title","Empirical risk minimization as parameter choice rule for general linear regularization methods"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["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","3569"],["dc.bibliographiccitation.issue","6B"],["dc.bibliographiccitation.journal","The Annals of Statistics"],["dc.bibliographiccitation.lastpage","3602"],["dc.bibliographiccitation.volume","46"],["dc.contributor.author","Proksch, Katharina"],["dc.contributor.author","Werner, Frank"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:50:35Z"],["dc.date.available","2017-09-07T11:50:35Z"],["dc.date.issued","2018"],["dc.description.abstract","In this paper we propose a multiscale scanning method to determine active components of a quantity f w.r.t. a dictionary U from observations Y in an inverse regression model Y=Tf+ξ with linear operator T and general random error ξ. To this end, we provide uniform confidence statements for the coefficients ⟨φ,f⟩, φ∈U, under the assumption that (T∗)−1(U) is of wavelet-type. Based on this we obtain a multiple test that allows to identify the active components of U, i.e. ⟨f,φ⟩≠0, φ∈U, at controlled, family-wise error rate. Our results rely on a Gaussian approximation of the underlying multiscale statistic with a novel scale penalty adapted to the ill-posedness of the problem. The scale penalty furthermore ensures weak convergence of the statistic's distribution towards a Gumbel limit under reasonable assumptions. The important special cases of tomography and deconvolution are discussed in detail. Further, the regression case, when T=id and the dictionary consists of moving windows of various sizes (scales), is included, generalizing previous results for this setting. We show that our method obeys an oracle optimality, i.e. it attains the same asymptotic power as a single-scale testing procedure at the correct scale. Simulations support our theory and we illustrate the potential of the method as an inferential tool for imaging. As a particular application we discuss super-resolution microscopy and analyze experimental STED data to locate single DNA origami."],["dc.identifier.arxiv","1611.04537"],["dc.identifier.doi","10.1214/17-AOS1669"],["dc.identifier.gro","3145901"],["dc.identifier.issn","0090-5364"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3636"],["dc.language.iso","en"],["dc.notes.intern","lifescience"],["dc.notes.intern","Not valid abstract: In this paper we propose a multiscale scanning method to determine active components of a quantity $f$ w.r.t. a dictionary $\\\\.mathcal{U}$ from observations $Y$ in an inverse regression model $Y=Tf+\\\\.xi$ with operator $T$ and general random error $\\\\.xi$. To this end, we provide uniform confidence statements for the coefficients $\\\\.langle \\\\.varphi, f\\\\.rangle$, $\\\\.varphi \\\\.in \\\\.mathcal U$, under the assumption that $(T^*)^{-1} \\\\.left(\\\\.mathcal U\\\\.right)$ is of wavelet-type. Based on this we obtain a decision rule that allows to identify the active components of $\\\\.mathcal{U}$, i.e. $\\\\.left\\\\.langle f, \\\\.varphi\\\\.right\\\\.rangle \\\\.neq 0$, $\\\\.varphi \\\\.in \\\\.mathcal U$, at controlled, family-wise error rate. Our results rely on a Gaussian approximation of the underlying multiscale statistic with a novel scale penalty adapted to the ill-posedness of the problem. The important special case of deconvolution is discussed in detail. Further, the pure regression case, when $T = \\\\.ext{id}$ and the dictionary consists of moving windows of various sizes (scales), is included, generalizing previous results for this setting. Simulations support our theory and we illustrate the potential of the method as an inferential tool for imaging. As a particular application we discuss super-resolution microscopy and analyze experimental STED data to locate single DNA origami."],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.subject","multiscale analysis scan statistic ill-posed problem deconvolution super-resolution"],["dc.title","Multiscale scanning in inverse problems"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]