Locally Supported Orthogonal Wavelet Bases on the Sphere via Stereographic Projection
Joint Authors
Antoine, Jean-Pierre
Roşca, Daniela
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-10-18
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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 L2 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.
American Psychological Association (APA)
Roşca, Daniela& Antoine, Jean-Pierre. 2009. Locally Supported Orthogonal Wavelet Bases on the Sphere via Stereographic Projection. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-13.
https://search.emarefa.net/detail/BIM-447549
Modern Language Association (MLA)
Roşca, Daniela& Antoine, Jean-Pierre. Locally Supported Orthogonal Wavelet Bases on the Sphere via Stereographic Projection. Mathematical Problems in Engineering No. 2009 (2009), pp.1-13.
https://search.emarefa.net/detail/BIM-447549
American Medical Association (AMA)
Roşca, Daniela& Antoine, Jean-Pierre. Locally Supported Orthogonal Wavelet Bases on the Sphere via Stereographic Projection. Mathematical Problems in Engineering. 2009. Vol. 2009, no. 2009, pp.1-13.
https://search.emarefa.net/detail/BIM-447549
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447549