Confidence regions for images observed under the Radon transform

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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.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.identifier.urihttp://hdl.handle.net/2003/31822
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-423
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

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