The Annals of Statistics

Efficient estimation of a density in a problem of tomography

Laurent Cavalier

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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.

Article information

Ann. Statist., Volume 28, Number 2 (2000), 630-647.

First available in Project Euclid: 15 March 2002

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Zentralblatt MATH identifier

Primary: 44A12: Radon transform [See also 92C55] 62G05: Estimation

Radon transform nonparametric minimax estimators


Cavalier, Laurent. Efficient estimation of a density in a problem of tomography. Ann. Statist. 28 (2000), no. 2, 630--647. doi:10.1214/aos/1016218233.

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