Polar FT and Quasi-PolarFFT Basis idea

[garrettwrong]

I found two relevant papers (among several others) to our discussion this morning.

The first one summarizes and includes some relevant graphics of some polar Fourier basis functions, from the continuous perspective.

https://lmb.informatik.uni-freiburg.de/Publications/2008/WRB08/wa_report01_08.pdf

This second paper specifically discusses the practical complications of bandlimited polar FT on discrete data, lack of obvious polar FFT, and proposes a sort of interesting quasi polar FFT, which could be suitable for a Basis. (It supports round trips...). FWIW it reminds me a little of what we're doing for FB, with different motivation for points/weights...

Also they discuss at least one of the potential issues I think we were seeing in our dev meeting today... (support/bandlimit/sampling/aliasing).

https://www.cs.tau.ac.il/~amir1/PS/30_PolarFFT_SIAM_SISC.pdf

Maybe something(s) we can look at in the future. The reference collection in both these paper appear to be excellent. If we find any other gems on the topic let's add them to this discussion.

[garrettwrong]

Following up.

I asked Yoel if there is any reason to explore the alternative polar 2d transform implementations (one of which he wrote). He suggested that what we are doing via NUFFT is superior for the common lines application, but that there may be analogous improvements to be had in some 3D application. However, I think 3D is out of scope right now, since this effort is mainly to review/strengthen the 2D common line application. Maybe next time :).