  We study the non-parametric estimation of a multidimensional unknown density
f in a tomography problem based on independent and identically distributed
observations, whose common density is proportional to the Radon transform of f.
We identify the underlying statistical inverse problem and use a spectral
cut-off regularisation to deduce an estimator. A fully data-driven choice of
the cut-off parameter m in R+ is proposed and studied. To discuss the
bias-variance trade off, we consider Sobolev spaces and show the
minimax-optimality of the spectral cut-off density estimator. In a simulation
study, we illustrate a reasonable behaviour of the studied fully data-driven
estimator.
