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{1016218233,
author = {Cavalier, Laurent},
title = {Efficient estimation of a density in a problem of
tomography},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 630-647},
language = {en},
url = {http://dml.mathdoc.fr/item/1016218233}
}
Cavalier, Laurent. Efficient estimation of a density in a problem of
tomography. Ann. Statist., Tome 28 (2000) no. 3, pp. 630-647. http://gdmltest.u-ga.fr/item/1016218233/