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Nonequispaced fast Fourier transform
NFFT on SO(3)
NFSFT

# NFSOFT - NFFT on the rotation group

This algorithms calculate the fast Fourier synthesis and its adjoint on the rotation group for arbitrary sampling sets. They are based on the fast Fourier transform for nonequispaced nodes on the three-dimensional torus. Our algorithms evaluate the Fourier synthesis and its adjoint, respectively, of -bandlimited functions at arbitrary input nodes.

This library of C functions computes evaluates a function with finite orthogonal expansion

in terms of Wiegner-D functions on a set of arbitary nodes , , , in Euler angles. Furthermore, the fast evaluation of sums

for given function values and all indices .

The algorithms are implemented by Antje Vollrath in ./kernel/nfsoft. Related papers are

Gräf, M., Potts, D.
Sampling sets and quadrature formulae on the rotation group.
Numer. Funct. Anal. Optim. 30, 665 - 688,   (full paper ps, pdf),   2009

Potts, D., Prestin J., Vollrath A.
A Fast algorithm for nonequispaced Fourier transforms on the rotation group.
Numer. Algorithms, 52, 355 - 384,   (full paper ps, pdf),   2009

Hielscher, R., Potts, D., Prestin, J., Schaeben, H., Schmalz, M.
The Radon transform on SO(3): A Fourier slice theorem and numerical inversion.
Inverse Problems 24, 025011,   (full paper ps, pdf),   2008