A fast algorithm for nonequispaced Fourier transforms on the rotation group

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+B⁴)\mathcal O(M+B^4) or even O(M + B³ log² B)\mathcal O(M + B^3 \log^2 B) flops instead of O(MB³)\mathcal O(MB^3). Numerical results will be presented establishing the algorithm’s numerical stability and time requirements.