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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

Abstract

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.

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Laurent Cavalier. "Efficient estimation of a density in a problem of tomography." Ann. Statist. 28 (2) 630 - 647, April 2000. https://doi.org/10.1214/aos/1016218233

Information

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

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

Subjects:
Primary: 44A12, 62G05

Rights: Copyright © 2000 Institute of Mathematical Statistics

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