Localized spherical deconvolution

Details Localized spherical deconvolution Localized spherical deconvolution

2009-08-13

arxiv.org/abs/0908.1952v2

Annals of Statistics 2011, Vol. 39, No. 2, 1042-1068

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS858 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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