Direct Fourier Inversion (gridrec algorithm)

In contrast to the Filtered Back-Projection (FBP) algorithm, Direct Fourier Inversion (DFI, sometimes called re-gridding algorithm) uses the Fourier-slice theorem to reconstruct a slice from the sinogram. This method is much faster (\(O(N^2 \log(N))\) instead of \(O(N^3)\)) but suffers from the drawback of having to interpolate between polar space to cartesian space. This interpolation is tricky when we go far from the center, as only few samples in the polar space are available ; and any interpolation “error” in the Fourier space induces errors everywhere in the reconstructed image.

Using this method makes sense when enough projections are available: the quality is barely the same between FBP and DFI in this case, although DFI being much faster.

Here is a standard configuration for using DFI:

FBFILTER = 10 # on recent versions, DSE_DFI = 1 can be used
DFI_KERNEL_SIZE=7
DFI_NOFVALUES=1024
DFI_OVERSAMPLING_RATE=1
DFI_R2C_MODE=YES