I am trying to understand for what cases and in what way NUFFTs would be useful for CT reconstruction. Therefore, I am trying to create an overview for myself that starts with the "easy" problems where we can apply FFT and ends with the hardest cases. I could then determine which method would be appropriate for my problem. I am having trouble finding a source that outlines nicely what the differences between FFT, NFFT, NUFFT and USFFT (or others that I don't know about) are.

The way I currently see it is that we can split reconstruction methods along the Fourier slice theorem. We can either define the dual transform of the Radon transform (filtered backprojection) or we can use the 2D Fourier transform along radial lines and obtain sample points in 2D Fourier space. We then get a polar raster of sample points.

At this point I want to understand the different methods that can be used to reconstruct my original function from these sample points in Fourier space. I understand that there are various interpolation methods we can use to place sample points on the Cartesian grid for FFT but it is unclear to me if this is already one of the above abbreviations (NFFT etc.). I feel that these terms are mixed and overloaded often and sometimes refer to algorithms and sometimes refer to general concepts. I think it would be helpful if it became clear what exactly is what in this field. If anyone can explain this to me or can recommend a source it would be greatly appreciated.

Note: Ultimately, I want to improve reconstructions for electron tomography data with missing angles, i.e. they only measure from 30 to 150 degrees, if this is useful information.


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