## How to guess imaginary part of picture when deconvolving ?

### How to guess imaginary part of picture when deconvolving ?

In working with our imageprocessing software I have noticed this:

If one convolves a sharp image with some PSF, what you realy get is
a image (blurred) with a imaginary part. The imaginary part get lost
when stored as a ordinary image. That means that you cant get back
to the exact (sharp) original because you have lost information. In fact
(?) when dividing the fft (of the blurred image) with the fft of the
psf what I get is completely unusable, I have to restrict the division
to point not to far from the center (of the fft's). The result is
phenomenal (in my mind) but its not as good as the original; it's
greyer and there is some ringing.

Now the question is:
a) is there some way of making a good guess to better the process
b) perheps it's (theoretcally) possible to synthesize the imaginary part
of the image from the psf (if one know it apriori) and the real part of
the blurred image. At least when it comes to cameras and lenses (or a
boxcamera) it would be possible to KNOW the full info about the psf.

Compare these two scenarios

1  you have a blurred photo where one blur is known to come from a point
source.

2: You have  a blurred photo and psfinfo about the blurring proceess (you
also know the imaginary part)

Since in 2 you know more - namely ifo about the imaginary part of the psf -
it must be possible to deblurr the image more effectively ?

The question is how ?

Can someone fill me in ?

Pelle

PS If anyone whants to have a look at the software (with some example images)

### How to guess imaginary part of picture when deconvolving ?

I believe you can reconstruct the imaginary part in some special cases
with something called the Hilbert Transform.  I don't recall all the
particular conditional requirements, but I've used it successfully in
some 1-D signal processing.  I don't know about extending it to 2D, but
it should be possible.  You should be able to find references to it in
most basic digital signal processing textbooks.

I don't have my notes and text with me at the moment, but I can dig them

Doug

--
Doug Childers
Imaging Scientist
GDE Systems Inc.
phone: (619) 592-5485

### How to guess imaginary part of picture when deconvolving ?

B.Boashash, Estimating and Interpreting The Instantaneous Frequency of a
Signal - Part 1: Fundamentals, Proceedings of the IEEE, vol.80, no.4,
pp.520-538, April 1992

it is stated that Gabor introduced a method for making a unique complex
signal from a real one. In time-domain:

z(t) = s(t) + iH[s(t)]
= a(t)e^[if(t)]

where z(t) is Gabor's complex signal, s(t) is the real signal and H[]
denotes the Hilbert transform. Gabor's work may be found in:

D.Gabor, Theory of Communication, Proceedings
of the IEE, vol.93(III), pp.429-457, 1946

Hope this helps!

Marcus
---

http://www.hut.fi/~mengdahl/index.html

What is the easiest way to plot the real and imaginary parts of complex
data using gnuplot, i.e., here's a sample file:

1  2.800000 (-2.2727976E-02,3.3804771E-02) (-13.69713,-20.37262)
1  2.900000 (-1.5100162E-02,2.4222020E-02) (-18.53415,-29.73044)
1  3.000000 (-1.1429808E-02,1.7317461E-02) (-26.54792,-40.22312)
1  3.100000 (-9.5665818E-03,1.2080790E-02) (-40.28629,-50.87399)

I want to plot the real part of column 4 against column 2.  I have a GKS
based program which easily handles this but I can't figure out how to make
gnuplot do it and I don't have GKS on any of my present machines.

I'm running gnuplot 3.5 on an SGI under IRIX 5.3, should I upgrade to 3.6
or is it still in beta and how unstable is it.

+------------------------------------------------------------------------+
| Michael S. Kluskens                Office: 202/404-1818                |
| Radar Division, Code 5316          FAX:    202/767-6276                |
| Naval Research Laboratory                                              |

+------------------------------------------------------------------------+