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A fast algorithm for nonequispaced Fourier transforms on the rotation group

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Abstract

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

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Authors and Affiliations

  1. Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany

    Daniel Potts

  2. Institute of Mathematics, University of Lübeck, Lübeck, Germany

    Jürgen Prestin & Antje Vollrath

  3. Lübeck Graduate School for Computing in Medicine and Life Sciences, Lübeck, Germany

    Antje Vollrath

Authors
  1. Daniel Potts
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  2. Jürgen Prestin
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  3. Antje Vollrath
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Correspondence to Daniel Potts.

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Potts, D., Prestin, J. & Vollrath, A. A fast algorithm for nonequispaced Fourier transforms on the rotation group. Numer Algor 52, 355–384 (2009). https://doi.org/10.1007/s11075-009-9277-0

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  • DOI: https://doi.org/10.1007/s11075-009-9277-0

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