Wavelets on the sphere: implementation and approximations
type: Item
instance of: scholarly article
title: Wavelets on the sphere: implementation and approximations
zbMATH Open document ID: 1021.42022
DOI: 10.1016/S1063-5203(02)00507-9
published in: Applied and Computational Harmonic Analysis
publication date: 2003-04-02T00:00:00Z
review text: The authors continue the analysis of the continuous wavelet transform (CWT) on the 2-sphere, introduced by \textit{J.-P. Antoine} and \textit{P. Vandergheynst} [Appl. Comput. Harmon. Anal. 7, No. 3, 262-291 (1999; Zbl 0945.42023)]. First, they discuss directional spherical wavelets, i.e., spherical wavelets that are sensitive to directions. Using fast Fourier transforms, the authors compute spherical CWT for data given on a regular spherical grid. Numerical examples are presented. Finally, they establish conditions under which a reconstruction formula of the spherical CWT holds in strong \(L^p\) topology with \(1\leq p<\infty\).
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 1891400
zbMATH Keywords: continuous wavelet transform
zbMATH Keywords: 2-sphere
zbMATH Keywords: directional spherical wavelet
zbMATH Keywords: approximate identity
zbMATH Keywords: fast algorithm
zbMATH Keywords: reconstruction formula
author: J. P. Antoine
author: Laurent Demanet
author: Laurent Jacques
author: P. Vandergheynst
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891400