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dc.contributor.authorBissantz, Nicolai-
dc.contributor.authorHolzmann, Hajo-
dc.contributor.authorProksch, Katharina-
dc.date.accessioned2014-01-14T08:51:42Z-
dc.date.available2014-01-14T08:51:42Z-
dc.date.issued2014-01-14-
dc.identifier.urihttp://hdl.handle.net/2003/31822-
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-423-
dc.description.abstractRecovering a function f from its integrals over hyperplanes (or line integrals in the two-dimensional case), that is, recovering f from the Radon transform Rf of f, is a basic problem with important applications in medical imaging such as computerized tomography (CT). In the presence of stochastic noise in the observed function Rf, we shall construct asymptotic uniform confidence regions for the function f of interest, which allows to draw conclusions regarding global features of f. Speci cally, in a white noise model as well as a fixed-design regression model, we prove a Bickel-Rosenblatt-type theorem for the maximal deviation of a kernel-type estimator from its mean, and give uniform estimates for the bias for f in a Sobolev smoothness class. The finite sample properties of the proposed methods are investigated in a simulation study.en
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB 823;02/2014-
dc.subjectconfidence bandsen
dc.subjectradon transformen
dc.subjectnonparametric regressionen
dc.subjectinverse problemsen
dc.subject.ddc310-
dc.subject.ddc330-
dc.subject.ddc620-
dc.titleConfidence regions for images observed under the Radon transformen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access-
Appears in Collections:Sonderforschungsbereich (SFB) 823

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