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.
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. Related paper are
Fenn, M., Kunis, S., and Potts, D. On the computation of the polar FFT.
Appl. Comput. Harm. Anal. 22, 257-263, (full paper
Böttcher, A. and Potts, D. Probability against condition number and sampling of multivariate trigonometric random polynomials. Electron. Trans. Numer. Anal. , 26, 178-189, (full paper
Böttcher, A., Potts, D. and Wenzel, D A probability argument in favor of ignoring small singular values.
Operator Theory: Advances and Applications, 1, 31-43, (full paper