Once we have an FBP algorithm, there should be no problem at all to obtain a convolution backprojection algorithm. All we have to do is to take the inverse Fourier transform of the weighted ramp filter to get a convolution kernel.
This is easier said than done. The problem is that we have a closed-form expression for the frequency domain transfer function for the windowed ramp filter; however, we do not have a closed-form expression for the spatial domain convolution kernel. Numerical evaluation of the convolution kernel costs time.
Fig. 8.6: FBP reconstruction results using dynamic MRI data. Top: Reconstructions ...