Localized spherical deconvolution
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 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.
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)