[futurebasic] [X-FB] Wiener Optimum Filtering

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From: Herbie Gluender <H.Gluender@...>
Date: Tue, 18 Dec 2001 12:24:39 +0100
Dear Tedd,

first I must tell you that I don't have any code for Wiener filtering.

When I did Wiener filtering (named after Norbert Wiener, a mathematician at
the MIT who became famous for his work in statistics and control theory as
well as the founder of an interesting but later misused field called
cybernetics) I was using a quite unusual technique, namely coherent optical
analog computing which actually realizes linear filters in the Fourier Domain.
With this technique the analog FT is the diffraction pattern of the image or
signal to be processed. A nice but not very flexible technique that doesn't
suffer from the shortcomings of the discrete FT approaches such as FFT (the
windowing problem was mentioned recently, but there are many more problems
such as aliasing)! Back then, we did (not only but to a great extent and with
much success) Wiener Optimum filtering of medical scintigrams. These are
diagnostic images from nuclear medicine that suffer from heavy Gaussian blur
and extreme photon noise. This is a convenient application for Wiener
corrected inverse filtering because the inverse filter is real valued. The
Wiener correction must be derived from the signal/noise-ratio in the images
and this is a difficult issue in the case of scintigrams because the noise is
signal dependent, not additive. This means, in the strict sense, that you are
not allowed to use linear Wiener Optimum filters. However, we could show that
many images can be restored in good approximation by this approach. The
filters were realized as photographic transparencies and put in the Fourier
Plane of a coherent optical processor. Then the computation was performed, so
to say at the speed light... The filer result, i.e. the filtered image, either
was recorded photographically or by a TV-camera.

Second, I'm not quite sure whether I would use the term tapper with respect to
Wiener filters, because they must be tailored according to the _spectral_
noise power that is present in the signals to be processed...

Third, and this is not at all addressed to Tedd:
I apologize for anything I've done wrong to the list recently and my apologies
for this off-topic post. Please would everybody who became annoyed by my
recent posts tell me that _offlist_ in a clear-cut fashion so that I can
change my bad habits.

Best to all of you and thanks for your question Tedd.

Herbie
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H.Glu@...