SFB 823 Confidence regions for images observed under the Radon transform

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 tomog-raphy (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. Specifically, 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.