## The Annals of Statistics

### Efficient estimation of a density in a problem of tomography

Laurent Cavalier

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 15 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1016218233

Digital Object Identifier
doi:10.1214/aos/1016218233

Mathematical Reviews number (MathSciNet)
MR1790012

Zentralblatt MATH identifier
1105.62331

Subjects

#### Citation

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. https://projecteuclid.org/euclid.aos/1016218233

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