Inversion of noisy Radon transform by SVD based needlets
Date
2010ISSN
1063-5203Source
Applied and Computational Harmonic AnalysisVolume
28Issue
1Pages
24-45Google Scholar check
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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.