Open Access
April 2011 Localized spherical deconvolution
Gérard Kerkyacharian, Thanh Mai Pham Ngoc, Dominique Picard
Ann. Statist. 39(2): 1042-1068 (April 2011). DOI: 10.1214/10-AOS858


We provide a new algorithm for the treatment of the deconvolution problem 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 behavior of our procedure for any $\mathbb {L}_{p}$ 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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Gérard Kerkyacharian. Thanh Mai Pham Ngoc. Dominique Picard. "Localized spherical deconvolution." Ann. Statist. 39 (2) 1042 - 1068, April 2011.


Published: April 2011
First available in Project Euclid: 8 April 2011

zbMATH: 1216.62059
MathSciNet: MR2816347
Digital Object Identifier: 10.1214/10-AOS858

Primary: 62G05 , 62G08 , 62G10 , 62G20

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

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 2 • April 2011
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