Open Access
May 2012 Radon needlet thresholding
Gérard Kerkyacharian, Erwan Le Pennec, Dominique Picard
Bernoulli 18(2): 391-433 (May 2012). DOI: 10.3150/10-BEJ340


We provide a new algorithm for the treatment of the noisy inversion of the Radon transform using an appropriate thresholding technique adapted to a well-chosen new localized basis. We establish minimax results and prove their optimality. In particular, we prove that the procedures provided here are able to attain minimax bounds for any $\mathbb {L}_{p}$ loss. It is important to notice that most of the minimax bounds obtained here are new to our knowledge. It is also important to emphasize the adaptation properties of our procedures with respect to the regularity (sparsity) of the object to recover and to inhomogeneous smoothness. We perform a numerical study that is of importance since we especially have to discuss the cubature problems and propose an averaging procedure that is mostly in the spirit of the cycle spinning performed for periodic signals.


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Gérard Kerkyacharian. Erwan Le Pennec. Dominique Picard. "Radon needlet thresholding." Bernoulli 18 (2) 391 - 433, May 2012.


Published: May 2012
First available in Project Euclid: 16 April 2012

zbMATH: 1243.65152
MathSciNet: MR2922455
Digital Object Identifier: 10.3150/10-BEJ340

Keywords: minimax estimation , second-generation wavelets , Statistical inverse problems

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability

Vol.18 • No. 2 • May 2012
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