# Inversion of noisy Radon transform by SVD based needlet

Abstract : 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.
Document type :
Journal articles
Applied and Computational Harmonic Analysis, Elsevier, 2010, 28 (1), pp.24-45
Domain :
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00321894
Contributor : Erwan Le Pennec <>
Submitted on : Monday, August 17, 2009 - 11:58:46 AM
Last modification on : Monday, May 29, 2017 - 2:27:13 PM
Document(s) archivé(s) le : Wednesday, September 22, 2010 - 12:48:05 PM

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### Identifiers

• HAL Id : hal-00321894, version 2
• ARXIV : 0809.3332

### Citation

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, Elsevier, 2010, 28 (1), pp.24-45. <hal-00321894v2>

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