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From: adorf@eso.org (Hans-Martin Adorf)
Subject: Re: Image Recovery Question
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Date: Fri, 31 Mar 1995 13:56:45 +0100
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In article <3lflo3$sc5@nuscc.nus.sg>, mpengtw@leonis.nus.sg (Ng Tuck Wah) wrote:

> Suppose that I have an image that is degraded by noise but I know where 
> they are on the image (by the way, they are randomly located); is it 
> possible to recover the original image by filling in the bad points by 
> approximating from the values from the good points? Would appreciate it if 
> anyone could point to some related work. Thanx.

This is a problem typical for image reconstruction/restoration with
missing data. You have to have some prior knowledge, such as the
point-spread function or a band-limit, which helps to substitute for the
missing data values. We in the Hubble Space Telescope project have some
experience with "restoration with missing data", and I can recommend the
POCS method (works without a PSF), and a generalisation of the
Richardson-Lucy method (requires a PSF).

For reference see e.g. 

Adorf, H.-M.: 1994, Towards HST image restoration with a space variant
PSF, cosmic rays, and other missing data, in: Proc. The restoration of
HST images and spectra II, 1819 Nov 1993, Baltimore, MD 21218, R.J.
Hanisch and R.L. White (ed.), Space Telescope Science Institute & NASA,
pp. 7278.

Adorf, H.-M.: 1995, POCS image combination, ST-ECF Newslett. 22, 1619.

Adorf, H.-M., Hook, R.N., Lucy, L.B.: 1993, Restoration of HST images and
spectra  some lessons learnt, in: Proc. SPIE Int. Symp. OE/Aerospace
Science and Sensing 93", Techn. Conf. "Space Astronomical Telescopes and
Instrumentation II, Orlando, Florida, 1216 April 1993, P.Y. Bly and
J.B. Breckinridge (ed.), SPIE, pp. 7582.

Freudling, W.: 1995, An image restoration technique for the removal of
cosmic ray hits from dithered images, Publ. Astron. Soc. Pacific 107,
8589.

Medoff, B.P., Brody, W.R., Nassi, M., Macovski, A.: 1983, Iterative
convolution backpropagation algorithms for image reconstruction from
limited data, J. Opt. Soc. America .

Tanner, M.M.: Tools for Statistical Inference. Observed Data and Data
Augmentation Methods, in: Lecture Notes in Statistics, Springer-Verlag,
New York.

White, R.L.: 1993, Improvements to the Richardson-Lucy method, in:
Restoration - Newsletter of the STScI's Image Restoration Project, B.
Hanisch (ed.), Space Telescope Science Institute, 1819 Nov 1993,
Baltimore, MD 21 218, pp. 1122.

Regards
Hans-Martin Adorf

-- 
Hans-Martin Adorf
ST-ECF/ESO
Karl-Schwarzschild-Str. 2
D-85748 Garching b. Muenchen
Germany
Tel: +49-89-32006-261
Fax: +49-89-32006-480
Internet: adorf@eso.org
