Just a quick note to pass on a very informative answer
to my question about whether it is possible to de-smooth
smoothed BOLD images.
The answer was sent by Prof. Jeffrey Fessler of U.Michigan,
author of the Matlab Image Reconstruction Toolbox:
and author of many papers on MRI image reconstruction:
Although the answer isn't the one that I was hoping to hear,
it is pretty definitive.
---------- Forwarded message ----------
From: Jeffrey Fessler <[log in to unmask]>
Date: Fri, Mar 6, 2009 at 5:37 PM
Subject: Re: Q: How to de-smooth MRI images, previously smoothed with a known
To: Rajeev Raizada <[log in to unmask]>
Cc: Jeffrey Fessler <[log in to unmask]>
deblurring a gaussian is horribly ill conditioned.
i have a book chapter on image restoration that gives
more details about why inverse filtering is bad:
it is basically hopeless. for more bad news, see this:
@a philip:87:tmi invpro 3 2 309-28 may 1987
The most ill-posed non-negative kernels in discrete deconvolution
@u doi 10.1088/0266-5611/3/2/013
@an "The most ill-posed kernels are all similar to the binomial kernels,
which are discretisations of the gaussian"