Journal
NUMERICAL ALGORITHMS
Volume 52, Issue 3, Pages 355-384Publisher
SPRINGER
DOI: 10.1007/s11075-009-9277-0
Keywords
Rotation group; Spherical Fourier transform; Generalized spherical harmonics; Fourier synthesis; Wigner-D functions; Wigner-d functions; Fast discrete transforms; Fast Fourier transform at nonequispaced nodes
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Funding
- Deutsche Forschungsgemeinschaft [PO 711/9-1]
- Lubeck Graduate School for Computing in Medicine and Life Sciences
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In this paper we present algorithms to calculate the fast Fourier synthesis and its adjoint on the rotation group SO(3) for arbitrary sampling sets. They are based on the fast Fourier transform for nonequispaced nodes on the three-dimensional torus. Our algorithms evaluate the SO(3) Fourier synthesis and its adjoint, respectively, of B-bandlimited functions at M arbitrary input nodes in O(M + B-4) or even O(M + B-3 log(2) B) flops instead of O(MB3). Numerical results will be presented establishing the algorithm's numerical stability and time requirements.
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