Inversion of noisy Radon transform by SVD based needlet

Details Inversion of noisy Radon transform by SVD based needlet Inversion of noisy Radon transform by SVD based needlet

2008-09-19

arxiv.org/abs/0809.3332v2

Applied and Computational Harmonic Analysis 28, 1 (2010) 24-45

Mathematics

Statistics Theory

Scientific paper

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.

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