> is it possible that spatial smoothing results in different smoothed dataset
> when conducted in the spatial domain and in the frequency domain (made
> equivalent by setting cut-off freq = 1/FWHM)?
It is very possible. An image can be considered as a discrete representation
of a continuous function. An image is often convolved by summing over the
voxels, weighting each voxel by the height of the e.g. Gaussian at each
point. This does not consider how the data is interpolated between the
centres of the voxels. If this is considered, then the operation would be
treated as a proper integration. Convolving in Fourier space would take this
interpolation into consideration. Also, if you examine the function
spm_smoothkern.m, you will see that it generates a smoothing kernel that
assumes that the images are continuously interpolated.
Another difference relates to the boundary conditions. If you smooth via
Fourier transforms, then you assume that outside the FOV, you have the image
repeating ad infinitum in all directions. This boundary condition can be
incorporated into spatial (temporal) smoothing procedures, but it is normally
not the case (e.g. in SPM).
Best regards,
-John
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