• Bernoulli
  • Volume 18, Number 2 (2012), 391-433.

Radon needlet thresholding

Gérard Kerkyacharian, Erwan Le Pennec, and Dominique Picard

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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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Bernoulli Volume 18, Number 2 (2012), 391-433.

First available in Project Euclid: 16 April 2012

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minimax estimation second-generation wavelets statistical inverse problems


Kerkyacharian, Gérard; Le Pennec, Erwan; Picard, Dominique. Radon needlet thresholding. Bernoulli 18 (2012), no. 2, 391--433. doi:10.3150/10-BEJ340.

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