Hi Bruce
On Sat, Mar 07, 2009 at 11:20:31AM -0500, Bruce Fischl wrote:
> I'm pretty sure it is. You can think about Gaussian convolution as moving
> intensities around the image since the diffusion equation obeys an
> underlying conservation law. So any one voxel has its intensity "come from"
> other voxels in the image. Unfortunately there is nothing unique about it,
> so you don't know for example if the intensity came from a high value voxel
> far away or a moderately valued voxel nearby. The inverse diffusion
> equation is fundamentally ill-conditioned.
Being a physicist, I really like this way of putting things, and I think
it is indeed very clear, however the other picture (of multiplication in
k-space) does give another intuition.
> The k-space thing is probably only true in the limit of infinite
> support, etc..., but I haven't thought about it.
I know very little about signal processing, but could it be due to finite
sampling/FFT issues: the Fourrier transform of gaussian kernel extends
past the bounds of the FFT, and thus the picture is not exact.
If somebody could clarify the k-space picture, I would find it most
interesting, not because I doubt the result, but for the simple pleasure
of learning.
Thank you for the interesting discussion,
Gaël
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