Inversion of noisy Radon transform by SVD based needlets
نویسندگان
چکیده
Article history: Received 29 July 2008 Revised 29 May 2009 Accepted 3 June 2009 Available online 12 June 2009 Communicated by W.R. Madych 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 Lp (1 p ∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed. © 2009 Elsevier Inc. All rights reserved.
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