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arXiv · 0908.1952

Localized spherical deconvolution

Gérard Kerkyacharian·Thanh Mai Pham Ngoc·Dominique Picard
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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 $\mathbb {L}_p$ 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. 2009-08-13. Localized spherical deconvolution. https://doi.org/10.1214/10-aos858

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