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Nonequispaced fast Fourier transform
Polar FFT
Polar FFT

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.

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

oFenn, M., Kunis, S., and Potts, D.
On the computation of the polar FFT.
Appl. Comput. Harm. Anal. 22, 257-263,   (full paper ps, pdf),   2007

oB÷ttcher, A. and Potts, D.
Probability against condition number and sampling of multivariate trigonometric random polynomials.
Electron. Trans. Numer. Anal. , 26, 178-189,   (full paper ps, pdf),   2007

oB÷ttcher, 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 ps, pdf),   2007