Confidence regions for images observed under the Radon transform
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Date
2014-01-14
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Abstract
Recovering 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.
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Keywords
confidence bands, radon transform, nonparametric regression, inverse problems