Dear Geoff,
Can I just chime in with one or two comments:
> The question was raised as to what is the appropriate order for these
> manipulations of the data. I believe that the answer will always be that the
> slice correction step should be performed before the motion correction step.
> The rationale for this assertion is that motion correction disrupts the
> known absolute time at which a given data point was acquired. It is the fMRI
> slice in absolute space (and not the actual brain within that slice) that
> needs to be shifted in time.
I hope you don't mind me shifting your words around a little, but you could
also say that the slice-timing correction disrupts the known absolute
location at which a given data point was acquired. It is the fMRI slice in
absolute time that needs to be shifted in space.
Consider an fMRI dataset containing ascending slices where there was a
jump of 1 slice. What you do depends on what you consider to be the
greatest source of error: a timing error of 1 TR, or a spatial error
of one slice.
A four dimensional interpolation would be an improvement over the current two
step procedure, but this is just not practically feasible.
> Also, I don't believe that it is the case that using the middle slice
> affords any greater "accuracy" in making the correction. The slice
> correction routine makes the assumption that no meaningful power is present
> in the data above the Nyquist frequency. (For which there is some empirical
> support). Given this assumption, all shifts in time using sinc-interpolation
> are equally valid.
I don't think that there are any theoretical reasons why there should not
be any power above the Nyquist frequency. A typical HRF to a delta function
will contain frequencies higher than the frequency of the acquisition of
sucessive scans.
In practice, I suspect that using a middle slice as opposed to using the
first slice will probably make very little difference (providing that the
covariates are properly aligned).
Regards,
-John
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