Localized spherical deconvolution

Gérard Kerkyacharian (1) , Thanh Mai Pham Ngoc (1) , Dominique Picard (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We provide a new algorithm for the treatment of deconvolution 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 behaviour of our procedure for any Lp 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.

Mots clés: statistical inverse problems; minimax estimation; second- generation wavelets

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Gérard Kerkyacharian, Thanh Mai Pham Ngoc, Dominique Picard. Localized spherical deconvolution. Annals of Statistics, 2011, 39 (2), pp.1042-1068. ⟨hal-00409784⟩