On Fri, 6 Mar 2009 09:27:24 -0800, Michael T Rubens
<[log in to unmask]> wrote:
>take FFT of smoothed image, divided by FFT of gaussian. the inverse FFT
>should be your unsmoothed data.
Thanks...
But please see below... :-)
>On Fri, Mar 6, 2009 at 5:12 AM, Rajeev Raizada <[log in to unmask] wrote:
[...]
>> 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 :-)
I believe that the application of an inverse filter
may be easier said than done.
It appears that for Gaussian deblurring, the inverse is "ill-conditioned",
e.g. http://ieeexplore.ieee.org/iel5/5992/26914/01196312.pdf
Two additional complications:
1. Apparently there are some analytical results for deblurring of 2D discrete Gaussians,
but I don't know enough to know whether these hold in 3D as well.
2. I believe that the 3D smoothing is actually done by a Gaussian convolved
by a sinc function, not just a plain vanilla Gaussian.
Does anyone have an actual implementation of such "de-smoothing",
as opposed to an "in principle" description of what it ought to involve?
Googling for gaussian deblurring turns up a lot of hits for blind deconvolution
and methods of counteracting noise.
However, in this case the deconvolution is not blind at all,
as we know that it was a gaussian kernel of FWHM 6mm,
and also there wasn't any noise in the blurring process.
So, in principle those two facts ought to make things easier, I think?
Any help greatly appreciated.
The more specific the better. :-)
Raj
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