Constructing orthogonal wavelet bases on the sphere
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. Using this map, any plane wavelet may be lifted to a wavelet on the sphere. In...
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ftunivlouvain:oai:dial.uclouvain.be:boreal:75181 2024-05-12T08:08:35+00:00 Constructing orthogonal wavelet bases on the sphere Rosca, Daniela Antoine, Jean-Pierre 16th European Signal Processing Conference (EUSIPCO 2008) Technical University of Cluj-Napoca - Department of Mathematics UCL - SST/IRMP - Institut de recherche en mathématique et physique 2008 http://hdl.handle.net/2078.1/75181 eng eng EPFL boreal:75181 http://hdl.handle.net/2078.1/75181 info:eu-repo/semantics/openAccess info:eu-repo/semantics/conferenceObject 2008 ftunivlouvain 2024-04-17T17:28:17Z 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. Using this map, any plane wavelet may be lifted to a wavelet on the sphere. In this work we quickly review some existing constructions of spherical wavelets, then we apply the new procedure to orthogonal compactly supported wavelet bases in the plane and we get continuous, locally supported orthogonal wavelet bases on the sphere. As an example, we perform a singularity detection, where the other constructions of spherical wavelet bases fail. Conference Object North Pole South pole DIAL@UCLouvain (Université catholique de Louvain) North Pole South Pole |
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Open Polar |
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DIAL@UCLouvain (Université catholique de Louvain) |
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ftunivlouvain |
language |
English |
description |
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. Using this map, any plane wavelet may be lifted to a wavelet on the sphere. In this work we quickly review some existing constructions of spherical wavelets, then we apply the new procedure to orthogonal compactly supported wavelet bases in the plane and we get continuous, locally supported orthogonal wavelet bases on the sphere. As an example, we perform a singularity detection, where the other constructions of spherical wavelet bases fail. |
author2 |
Technical University of Cluj-Napoca - Department of Mathematics UCL - SST/IRMP - Institut de recherche en mathématique et physique |
format |
Conference Object |
author |
Rosca, Daniela Antoine, Jean-Pierre 16th European Signal Processing Conference (EUSIPCO 2008) |
spellingShingle |
Rosca, Daniela Antoine, Jean-Pierre 16th European Signal Processing Conference (EUSIPCO 2008) Constructing orthogonal wavelet bases on the sphere |
author_facet |
Rosca, Daniela Antoine, Jean-Pierre 16th European Signal Processing Conference (EUSIPCO 2008) |
author_sort |
Rosca, Daniela |
title |
Constructing orthogonal wavelet bases on the sphere |
title_short |
Constructing orthogonal wavelet bases on the sphere |
title_full |
Constructing orthogonal wavelet bases on the sphere |
title_fullStr |
Constructing orthogonal wavelet bases on the sphere |
title_full_unstemmed |
Constructing orthogonal wavelet bases on the sphere |
title_sort |
constructing orthogonal wavelet bases on the sphere |
publisher |
EPFL |
publishDate |
2008 |
url |
http://hdl.handle.net/2078.1/75181 |
geographic |
North Pole South Pole |
geographic_facet |
North Pole South Pole |
genre |
North Pole South pole |
genre_facet |
North Pole South pole |
op_relation |
boreal:75181 http://hdl.handle.net/2078.1/75181 |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1798851635513917440 |