Locally supported orthogonal wavelet bases on the sphere via stereographic projection
type: Item
instance of: scholarly article
title: Locally supported orthogonal wavelet bases on the sphere via stereographic projection
zbMATH Open document ID: 1180.94017
DOI: 10.1155/2009/124904
author: Daniela Roşca
author: J. P. Antoine
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
review text: Summary: The stereographic projection determines a bijection between the two-sphere, minus the North Pole, and the tangent plane at the South Pole. This correspondence induces a unitary map between the corresponding \(L^{2}\) spaces. This map in turn leads to equivalence between the continuous wavelet transform formalisms on the plane and on the sphere. More precisely, any plane wavelet may be lifted, by inverse stereographic projection, to a wavelet on the sphere. In this work we apply this procedure to orthogonal compactly supported wavelet bases in the plane, and we get continuous, locally supported orthogonal wavelet bases on the sphere. As applications, we give three examples. In the first two examples, we perform a singularity detection, including one where other existing constructions of spherical wavelet bases fail. In the third example, we show the importance of the local support, by comparing our construction with the one based on kernels of spherical harmonics.
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 5632434
Wikidata QID: Q58648869
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/124904
OpenAlex ID: W2083889113
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description: scientific article; zbMATH DE number 5632434