Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!tut.cis.ohio-state.edu!ucbvax!ernie.Berkeley.EDU!jwl
From: jwl@ernie.Berkeley.EDU (James Wilbur Lewis)
Newsgroups: comp.graphics
Subject: Re: Reconstruction of blurred images...
Message-ID: <29214@ucbvax.BERKELEY.EDU>
Date: 18 May 89 07:20:19 GMT
References: <579@rna.UUCP>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: jwl@ernie.Berkeley.EDU.UUCP (James Wilbur Lewis)
Organization: University of California, Berkeley
Lines: 50

In article <579@rna.UUCP> dan@rna.UUCP (Dan Ts'o) writes:
>
>	Can someone get me started on the topic of reconstructing blurred
>images ? Hopefully references and available programs.

Well, one approach you might want to look into is to deconvolve the 
image and blur function.  Let's assume you know the point-spread
function (i.e. what the blurred image of a single point would look
like).  It's not hard to show that the blurred image will be the
convolution of the raw image and the point-spread function.  Your
job is now to invert the convolution to get the raw image from the
blurred image and the point-spread function.  You can do this with
Fourier transforms -- a convolution in the spatial domain is identical
to a point-by-point multiplication in the frequency domain.  So the
algorithm is to take the Fourier transform of the blurred image,
divide out the Fourier transform of the PSF, and do the inverse FT
on the result to obtain the raw image.

There is one snag.  If the transform of the PSF has zeroes in it, 
information is lost in the blurring process, and you can't perfectly
recover the raw image.  Too bad, eh?  But you probably weren't
expecting miracles anyway... :-)   I guess when you do the division
you could just skip over any (frequency domain) points where 
FT(PSF) == 0.  

Oh yeah...I guess the PSF would have to be constant over the image
for this to work.

>	I understand that many schemes depend on knowing the characteristics
>of the blurring process, but not all. Although we can make a few guesses
>about our blurring process, just how bad are we off if we don't make any
>such assumptions ?

Hmmm.  Can you fudge it by looking for isolated features in the blurred image 
which correspond to point sources in the raw image?  That way you could
read the PSF right off the image.  You could probably also get some information
out of edges....in fact, if the PSF is radially symmetric, as it ought to be
for a process like defocusing,  a single edge of arbitrary orientation is 
probably as good as an isolated point.  (sheer conjecture on my part -- 
anyone know for sure?) 

references?  hmmm...ok...(digdigdig)...how about Gonzalez & Wintz, _Digital
Image Processing_?   

I've got some nifty 2-D FFT code (in C) if you need it.

Good luck!

-- Jim Lewis
   U.C. Berkeley