Dear SPM list,
I have some old scans from a few years ago
on which I am interested in trying out some unsmoothed analyses.
However, unfortunately my archive only contains
the smoothed BOLD images, because at the time I hadn't realised
that the unsmoothed ones might also be interesting.
I know the width of the smoothing kernel that was applied (6mm).
I believe (but am not totally sure, hence this question)
that Gaussian smoothing with a known kernel-width
should be a fully invertible operation.
It is just a bunch of linear summations, after all.
I would be very grateful to hear people's thoughts on:
(a) Is there a direct one-shot command for doing this?
If you have a specific example, then that would be even better! :-)
Non-specific high-level exhortations to recast the smoothing
as a 3D Fourier filter and then to apply the inverse filter
are also welcome, but probably won't be quite as useful :-)
(b) Although a de-smoothing ought to work in theory,
in practice it will probably have some imperfections,
e.g. maybe due to rounding errors etc.
Are those imperfections negligible, or problematic?
Any help gratefully appreciated,