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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