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Abstract: We provide a new algorithm for the treatment of the noisy inversion of theRadon transform using an appropriate thresholding technique adapted to awell-chosen new localized basis. We establish minimax results and prove theiroptimality. In particular, we prove that the procedures provided here are ableto attain minimax bounds for any $\mathbb {L} p$ loss. It s important to noticethat most of the minimax bounds obtained here are new to our knowledge. It isalso important to emphasize the adaptation properties of our procedures withrespect to the regularity sparsity of the object to recover and toinhomogeneous smoothness. We perform a numerical study that is of importancesince we especially have to discuss the cubature problems and propose anaveraging procedure that is mostly in the spirit of the cycle spinningperformed for periodic signals.

Autor: Gerard Kerkyacharian LPMA, Erwan Le Pennec LPMA, INRIA Saclay - Ile de France, LM-Orsay, Dominique Picard LPMA

Fuente: https://arxiv.org/

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