Open Access
Translator Disclaimer
April 2000 Efficient estimation of a density in a problem of tomography
Laurent Cavalier
Ann. Statist. 28(2): 630-647 (April 2000). DOI: 10.1214/aos/1016218233


The aim of tomography is to reconstruct a multidimensional function from observations of its integrals over hyperplanes. We consider the model that corresponds to the case of positron emission tomography. We have $n$ i.i.d.observations from a probability density proportional to $Rf$, where $Rf$ stands for the Radon transform of the density $f$.We assume that $f$ is an $N$-dimensional density such that its Fourier transform is exponentially decreasing. We find an estimator of $f$ which is asymptotically efficient; it achieves the optimal rate of convergence and also the best constant for the minimax risk.


Download Citation

Laurent Cavalier. "Efficient estimation of a density in a problem of tomography." Ann. Statist. 28 (2) 630 - 647, April 2000.


Published: April 2000
First available in Project Euclid: 15 March 2002

zbMATH: 1105.62331
MathSciNet: MR1790012
Digital Object Identifier: 10.1214/aos/1016218233

Primary: 44A12 , 62G05

Keywords: nonparametric minimax estimators , Radon transform

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 2 • April 2000
Back to Top