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Wavelets on S3 and SO(3)—Their construction, relation to each other and Radon transform of wavelets on SO(3)

✍ Scribed by Swanhild Bernstein; Svend Ebert

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
385 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

The paper at hand is concerned with creating a flexible wavelet theory on the three sphere S 3 and the rotation group SO(3). The theory of zonal functions and reproducing kernels will be used to develop conditions for an admissible wavelet. After explaining some preliminaries on group actions and some basics on approximation theory, we will prove reconstruction formulas of linear and bilinear wavelet transformed L 2 -functions on S 3 . Moreover, specific examples will be constructed and visualized. Second, we deal with the construction of wavelets on the rotation group SO(3). It will be shown that the Radon transform of a wavelet packet on SO(3) gives a wavelet packet on S 2 for every fixed detection direction.

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