Localized spherical deconvolution

Abstract : We provide a new algorithm for the treatment of deconvolution on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the behaviour of our procedure for any Lp loss. It is important to emphasize the adaptation properties of our procedures with respect to the regularity (sparsity) of the object to recover as well as to inhomogeneous smoothness. We also perform a numerical study which proves that the procedure shows very promising properties in practice as well.
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Article dans une revue
Annals of Statistics, Institute of Mathematical Statistics, 2011, 39 (2), pp.1042-1068
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https://hal.archives-ouvertes.fr/hal-00409784
Contributeur : Thanh Mai Pham Ngoc <>
Soumis le : mercredi 12 août 2009 - 17:01:50
Dernière modification le : mardi 11 octobre 2016 - 13:48:10
Document(s) archivé(s) le : mardi 15 juin 2010 - 19:50:27

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  • HAL Id : hal-00409784, version 1

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Gérard Kerkyacharian, Thanh Mai Pham Ngoc, Dominique Picard. Localized spherical deconvolution. Annals of Statistics, Institute of Mathematical Statistics, 2011, 39 (2), pp.1042-1068. <hal-00409784>

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