Visualising 2D k-space and Fourier synthesis (1D & 2D, helps for image reconstruction and analysis)

Andrew Reader
Andrew Reader
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Published 2023-07-20
k-space, 2D Fourier transforms (analysis) and Fourier synthesis (inverse 2D Fourier transform)
Visualises radial trajectories in k-space, useful for subsequent understanding of the central section theorem, filtered backprojection, PET, CT and MRI image reconstruction
All Comments (5)
  • @055shubhamsonkar6
    Dear professor , I was never this much clear about the concepts, Thank you for this much effort in each videos . please share the slides for the videos , if possible.
  • @anatolicvs
    Dear Professor, I greatly admire your YouTube channel and have learned a lot from your valuable knowledge and techniques. Thank you for sharing your expertise with us. I'm particularly interested in the marvellous visualizations you use in your videos. Would it be possible to get access to the codes for these visuals?
  • @jaewonlee8147
    Hi Professor Reader, thanks for another great video! If you don't mind, I have a question about the sampling method you used for the Einstein picture reconstruction. Around 26:00, the sampling in k-space was done in a radial direction, and it very much reminded me of the CT image acquisition, where each projection is a slice in a 2D Fourier domain. In the case of FBP in CT image reconstruction, the argument is often that the lower frequency region is oversampled compared to the high frequency region, and we need to somehow normalize the sampling density by applying the ramp filter. So from the radial sampling of the Einstein picture, I expected to see something similar; as the sampling continues, we obtain a low-frequency enhanced image. However, it does not seem like the Einstein picture suffer from the overrepresentation of the low frequency samples. I am quite surprised and confused! Is there a reason why in this case the reconstruction is good without the ramp filter? Would we get better result with the ramp filter? Thanks.