Using NFFT3 - a software library for various nonequispaced fast Fourier transforms. NFFT 3 is a software library that implements the nonequispaced fast Fourier transform (NFFT) and a number of related algorithms, for example, nonequispaced fast Fourier transforms on the sphere and iterative schemes for inversion. This article provides a survey on the mathematical concepts behind the NFFT and its variants, as well as a general guideline for using the library. Numerical examples for a number of applications are given.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 58 articles , 1 standard article )

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  1. Barnett, Alex H.: Aliasing error of the (\exp(\beta\sqrt1-z^2)) kernel in the nonuniform fast Fourier transform (2021)
  2. Koga, Kazuki: Signal processing approach to mesh refinement in simulations of axisymmetric droplet dynamics (2021)
  3. Averseng, Martin: Fast discrete convolution in (\mathbbR^2) with radial kernels using non-uniform fast Fourier transform with nonequispaced frequencies (2020)
  4. Bartel, Felix; Hielscher, Ralf; Potts, Daniel: Fast cross-validation in harmonic approximation (2020)
  5. Lazarus, Carole; März, Maximilian; Weiss, Pierre: Correcting the side effects of ADC filtering in MR image reconstruction (2020)
  6. Rangan, Aaditya; Spivak, Marina; Andén, Joakim; Barnett, Alex: Factorization of the translation kernel for fast rigid image alignment (2020)
  7. Wülker, Christian: Fast SGL Fourier transforms for scattered data (2020)
  8. Xu, Boxi; Cheng, Jin; Leung, Shingyu; Qian, Jianliang: Efficient algorithms for computing multidimensional integral fractional Laplacians via spherical means (2020)
  9. Agaltsov, A. D.; Hohage, T.; Novikov, R. G.: An iterative approach to monochromatic phaseless inverse scattering (2019)
  10. Barnett, Alexander H.; Magland, Jeremy; af Klinteberg, Ludvig: A parallel nonuniform fast Fourier transform library based on an “exponential of semicircle” kernel (2019)
  11. Kircheis, Melanie; Potts, Daniel: Direct inversion of the nonequispaced fast Fourier transform (2019)
  12. Merhi, Sami; Zhang, Ruochuan; Iwen, Mark A.; Christlieb, Andrew: A new class of fully discrete sparse Fourier transforms: faster stable implementations with guarantees (2019)
  13. Adcock, Ben; Gataric, Milana; Hansen, Anders C.: Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples (2017)
  14. Benedetto, John J.; Nava-Tudela, Alfredo; Powell, Alexander M.; Wang, Yang: A frame reconstruction algorithm with applications to magnetic resonance imaging (2017)
  15. Börm, S.; Börst, C.; Melenk, J. M.: An analysis of a butterfly algorithm (2017)
  16. Caliari, M.; Ostermann, A.; Piazzola, C.: A splitting approach for the magnetic Schrödinger equation (2017)
  17. Chauffert, Nicolas; Ciuciu, Philippe; Kahn, Jonas; Weiss, Pierre: A projection method on measures sets (2017)
  18. Helou, Elias S.; Simões, Lucas E. A.: (\epsilon)-subgradient algorithms for bilevel convex optimization (2017)
  19. Hofmann, Michael; Nestler, Franziska; Pippig, Michael: NFFT based Ewald summation for electrostatic systems with charges and dipoles (2017)
  20. Jyh-Miin Lin: Python Non-Uniform Fast Fourier Transform (PyNUFFT): multi-dimensional non-Cartesian image reconstruction package for heterogeneous platforms and applications to MRI (2017) arXiv

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