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Computation of the polar FFT

The polar FFT is a special case of the NFFT, where one computes the Fourier transform on particular grids. Of course, the polar as well as a so-called pseudo-polar FFT can be computed very accurately and efficiently by the NFFT. Furthermore, the reconstruction of a $ 2d$ signal from its Fourier transform samples on a (pseudo-)polar grid by means of the inverse nonequispaced FFT is possible under certain density assumptions. For details see [21] and for further applications [3].

Figure 6.1: Left to right: polar, modified polar, and linogram grid of size $ R=16$ , $ T=32$ .
\includegraphics[width=0.3\textwidth]{images/polar_grid} \includegraphics[width=0.3\textwidth]{images/modified_polar_grid} \includegraphics[width=0.3\textwidth]{images/linogram_grid}



Jens Keiner 2006-11-20