Localized spherical deconvolution
Gérard Kerkyacharian, Thanh Mai Pham Ngoc, Dominique Picard
The Annals of Statistics · 2011 · Volume 39 · Issue 2
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.
Keywords
62G05, 62G08, 62G10, 62G20, minimax estimation, second generation wavelets, Statistical inverse problems
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