%0 Journal Article
%T Inversion of noisy Radon transform by SVD based needlet
%A G¨Śrard Kerkyacharian
%A George Kyriazis
%A Erwan Le Pennec
%A Pencho Petrushev
%A Dominique Picard
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0809.3332v2