Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!swrinde!zaphod.mps.ohio-state.edu!rpi!masscomp!peora!tarpit!bilver!alex
From: alex@bilver.uucp (Alex Matulich)
Newsgroups: comp.dsp
Subject: Why Don't My FFT Deconvolutions Work!!
Message-ID: <1991Feb9.034956.7993@bilver.uucp>
Date: 9 Feb 91 03:49:56 GMT
Distribution: na
Organization: W. J. Vermillion - Winter Park, FL
Lines: 41

I am doing a project that involves "sharpening up" a two-dimensional radar
scan of an object.  This, of course, requires a convolution.

I know that this is normally done for visual images by operating a 3x3
kernel over each pixel in the image, such as
       -1  0 -1
        0  5  0
       -1  0 -1
however, my response function is more than 3 pixels wide.  (In fact, it is
a _different size_ in the x and y dimensions because the waveguide used to
scan the object is rectangular and has different beamwidths in each
direction).

I don't have the faintest idea how to make an arbitrary-sized sharpening
kernel, and furthermore I am unclear on how to re-scale things after
I'm done.  I'm more comfortable with FFT's, anyway, and I can precisely
define my response function too.

You will recall that the deconvolution of a function f with a response
function g is

F(f decon g) = F(f) / F(g)

where F() is the Fourier transform.  See the problem?  You have to DIVIDE
by the Fourier transform of g.  In all my experiments, for any response
function I try, F(g) is zero somewhere (or near zero) which completely
messes up the result.

As a simple experiment I tried convolving some arbitrary 1-D signal with
a response function and then deconvolving it to see if I got back what I
started with.  The convolution always works perfectly.  The deconvolution
is junk.

TELL ME!  HOW IS THIS DONE, REALLY?  What can I do to make it work?
Thanks in advance -- email replies and I'll summarize.

-- 
 _ |__  Alex Matulich   (alex@bilver.UUCP)
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