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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.