Polar FFT

The polar as well as the pseudo-polar FFT can be computed very accurately and efficiently by the nonequispaced FFT. Furthermore, we apply the reconstruction of a 2d signal from its Fourier transform samples on a (pseudo-)polar grid by means of the inverse nonequispaced FFT.

Figure: Left to right: polar, modified polar, and linogram grid.

We demonstrated that one can compute polar/pseudo-polar FFTs and their inverses very efficiently and accurately.

The algorithms are implemented by Markus Fenn and Stefan Kunis in ./applications/polarFFT.

References

• Fenn, M., Kunis, S., and Potts, D.
  On the computation of the polar FFT.
  Appl. Comput. Harmon. Anal. 22, 257–263, 2007. pdf ps
• Böttcher, A. and Potts, D.
  Probability against condition number and sampling of multivariate trigonometric random polynomials.
  Electron. Trans. Numer. Anal. 26, 178–189, 2007. pdf ps
• Böttcher, A., Potts, D., and Wenzel, D.
  A probability argument in favor of ignoring small singular values.
  Operators and Matrices 1(1), 31–43, 2007. doi pdf ps