English

Localized spherical deconvolution

Statistics Theory 2016-08-14 v2 Statistics Theory

Abstract

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 Lp\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.

Keywords

Cite

@article{arxiv.0908.1952,
  title  = {Localized spherical deconvolution},
  author = {Gérard Kerkyacharian and Thanh Mai Pham Ngoc and Dominique Picard},
  journal= {arXiv preprint arXiv:0908.1952},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-21T13:35:18.092Z