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.
"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