Abstract
The paper at hand is concerned with creating a flexible wavelet theory on the three sphere S3 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 L2-functions on S3. 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 S2 for every fixed detection direction. Copyright © 2010 John Wiley & Sons, Ltd.
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