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 $R=16$ , $T=32$ .