  A linear method for inverting noisy observations of the Radon transform is
developed based on decomposition systems (needlets) with rapidly decaying
elements induced by the Radon transform SVD basis. Upper bounds of the risk of
the estimator are established in $L^p$ ($1\le p\le \infty$) norms for functions
with Besov space smoothness. A practical implementation of the method is given
and several examples are discussed.
