I am wondering the detail of the filtered backprojection.
Suppose I have a projection file:
[1 2 3 1 2]
Then to get its filtered backprojection version using ramp filter, I should
- apply FFT to it, to get its Fourier version $P(\omega,\theta)$
- To use |$\omega$| to multiply $P(\omega,\theta)$
I am a little confused at second step here.
Using the numeric example above, to apply FFT to
[1 2 3 1 2], we will get a complex sequence
9.0000 + 0.0000i -1.0000 - 1.1756i -1.0000 + 1.9021i -1.0000 - 1.9021i -1.0000 + 1.1756i
Should I apply |$\omega$| to both real and complex part of the sequence above, then do inverse FFT? Or should I only take the magnitude of above sequence, apply |$\omega$| to the magnitude, then do inverse FFT?
Either way, it seems I will get a complex sequence as the final results, but shouldn't the filtered projection be a real sequence? Anyone give me some pointers here? Thanks