Inversion of noisy Radon transform by SVD based needlet

Gérard Kerkyacharian (1) , George Kyriazis (2) , Erwan Le Pennec (1) , Pencho Petrushev (3, 4) , Dominique Picard (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 UCY - University of Cyprus [Nicosia]
3 Department of Mathematics [Columbia]
4 IMI, Department of Mathematics

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.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Gérard Kerkyacharian, George Kyriazis, Erwan Le Pennec, Pencho Petrushev, Dominique Picard. Inversion of noisy Radon transform by SVD based needlet. Applied and Computational Harmonic Analysis, 2010, 28 (1), pp.24-45. ⟨hal-00321894v2⟩