**AAS 201st Meeting, January, 2003**

*Session 63. Making it Work: Principled ``Model Free Deconvolution" via Multiscale Methods*

Special, Tuesday, January 7, 2003, 10:00-11:30am, 613-614
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## [63.04] Multiscale Methods and the Processing of Images Resulting from Counts

*A. Bijaoui, H. Bourdin, E. Slezak, G. Jammal (Obs. de la Cote d'Azur, France)*

Astrophysicists are often involved in the processing of
event counts: determination of the probability density
functions (PDF) of stellar parameters, estimation of the
galaxy density, restoration of an image obtained with a
counting detector. Under the assumption of statistical
independence of events, the empirical distribution is
perturbed by a Poisson noise. As this noise depends on the
bin scale, it is natural to introduce a mathematical
decomposition which takes into account this scale
characteristic. Thus, multiscale transforms and particularly
the wavelet ones appeared well-suited tools for processing
counts.

After a short description of the definition and properties
of the wavelet transforms, the ingredients for the
applications to counts will be reviewed: choice the wavelet
transform, PDF of the wavelet coefficients, thresholding and
softening functions (in particular in case of a Bayesian
approach), the regularized reconstruction and the inversion
algorithm in case of deconvolution. The Anscombe transform
will be introduced as an efficient mean for stabilizing the
variance. A step by step algorithm will be described.

Finally, some astrophysical applications will be given:
density of galaxies from their counts and restoration of
images observed with the X-ray satellite XMM-Newton.

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Bulletin of the American Astronomical Society, **34**, #4

© 2002. The American Astronomical Soceity.