Confidence regions for images observed under the Radon transform

JOURNAL OF MULTIVARIATE ANALYSIS

卷:128

Article

Bissantz, Nicolai¹  Holzmann, Hajo²  Proksch, Katharina¹ 

[1] Ruhr Univ Bochum, Fak Math, Bochum, Germany

[2] Univ Marburg, Fachbereich Math & Informat, D-35032 Marburg, Germany

关键词: Confidence bands;    Inverse problems;    Nonparametric regression;    Radon transform;   

DOI  :  10.1016/j.jmva.2014.03.005

来源: Elsevier

【 摘 要 】

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 off, 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 off. 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. (C) 2014 Published by Elsevier Inc.

【 授权许可】

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