Inversion of noisy Radon transform by SVD based needlet

Authors
Kerkyacharian, Gérard
Kyriazis, George
Pennec, Erwan Le
Petrushev, Pencho
Picard, Dominique
Description
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.
Keywords
Mathematics - Statistics Theory