Direct inversion of the three-dimensional pseudo-polar fourier transform

Amir Averbuch, Gil Shabat*, Yoel Shkolnisky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The pseudo-polar Fourier transform is a specialized nonequally spaced Fourier trans- form, which evaluates the Fourier transform on a near-polar grid known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other nonuniform sampling geometries is that the trans- formation, which samples the Fourier transform on the pseudo-polar grid, can be inverted using a fast and stable algorithm. For other sampling geometries, even if the nonequally spaced Fourier transform can be inverted, the only known algorithms are iterative. The convergence speed of these algorithms and their accuracy are dificult to control, as they depend both on the sampling ge- ometry and on the unknown reconstructed object. In this paper, a direct inversion algorithm for the three-dimensional pseudo-polar Fourier transform is presented. The algorithm is based only on one-dimensional resampling operations and is shown to be significantly faster than existing iterative inversion algorithms.

Original languageEnglish
Pages (from-to)A1100-A1120
JournalSIAM Journal of Scientific Computing
Issue number2
StatePublished - 2016


  • 3D pseudo-polar Fourier transform
  • Polar Fourier transform
  • Radon transform
  • Toeplitz matrices
  • Unequally spaced FFT


Dive into the research topics of 'Direct inversion of the three-dimensional pseudo-polar fourier transform'. Together they form a unique fingerprint.

Cite this