Filtered backprojection (FBP) for image reconstruction: central section theorem, Radon & Fourier

Paper: www.researchga...
Understanding the central section theorem.
Helps with the mathematics of filtered backprojection (FBP) image reconstruction for PET, MRI, CT and other imaging modalities.
Links the Fourier transform with the Radon transform.

[@davidbeckschulte8246]

Very good explanation!

[@AndrewJReader]

Thanks for the feedback!

[@chrtjune]

incredibly helpful video

[@AndrewJReader]

Many thanks for the helpful feedback

[@georgschramm6582]

Excellent explanation of the Fourier slice theorem and FBP with great visualizations, Andrew! Are you also planning a video on the pros and cons of FPB reconstruction in PET?

[@AndrewJReader]

Thanks so much Georg, really appreciate the feedback! In other videos on iterative reconstruction I think I have mentioned the pros and cons of FBP, and when I do updated videos on iterative reconstruction I will seek to remember to mention why, and why not, one would use FBP. Thanks for the suggestion.

[@anshuchoudhary5454]

Hello Andrew, thanks for the amazing video
I was constructing the image using LORs and then finding the interesction points of those straight lines. Is this a correct method ? Why is it less efficient ?

[@AndrewJReader]

Thanks for the feedback. It sounds like you are describing backprojection without filtering, is that right? (If so, perhaps worth checking this video: ruclips.net/video/XWvIXGAr6B4/видео.html). But if you are filtering, then backprojecting, that is fine. However, plotting just one value in the 2D k-space is equivalent to a whole line backprojection, and so a direct Fourier method is potentially more efficient. But interpolation in k-space needs great care, and so that's where things can potentially slow down.

[@anshuchoudhary5454]

Thanks for you reply @@AndrewJReader. Actually after using this method, my value of FWHM is coming out to be in 10 mm-15mm range which is large for detector like LSO. Though I am filtering it out initially. Will the fourier method gives better resolution ?

[@anshuchoudhary5454]

alright, i realised i was stupid back then. I was not doing the filtering right way.
Thank you professor

[@AndrewJReader]

@@anshuchoudhary5454 Hope the video was helpful!