21746 articles – 15574 Notices  [english version]

hal-00016328, version 2

## Nonparametric inference of photon energy distribution from indirect measurements

Eric Moulines 1, Francois Roueff 1, Antoine Souloumiac 2, Thomas Trigano () 3

Résumé : We consider a density estimation problem arising in nuclear physics. Gamma photons are impinging on a semiconductor detector, producing pulses of current. The integral of this pulse is equal to the total amount of charge created by the photon in the detector, which is linearly related to the photon energy. Because the inter-arrival of photons can be shorter than the charge collection time, pulses corresponding to different photons may overlap leading to a phenomenon known as pileup. The distortions on the photon energy spectrum estimate due to pileup become worse when the photon rate increases, making pileup correction techniques a must for high counting rate experiments. In this paper, we present a novel technique to correct pileup, which extends a method introduced in \cite{hall:park:2004} for the estimation of the service time from the busy period in M/G/$\infty$ models. It is based on a novel formula linking the joint distribution of the energy and duration of the cluster of pulses and the distribution of the energy of the photons. We then assess the performance of this estimator by providing an expression of its integrated square error. A Monte-Carlo experiment is presented to illustrate on practical examples the benefits of the pileup correction.

• 1 :  Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
• Télécom ParisTech – CNRS : UMR5141
• 2 :  Laboratoire d'Electronique et de Traitement du Signal (LETS)
• CEA : DRT/DETECS/SSTM/LETS
• 3 :  Hebrew University of Jerusalem (HUJ)
• Hebrew University of Jerusalem
• Domaine : Mathématiques/Statistiques
• Mots-clés : indirect observations – marked Poisson processes – nonlinear inverse problems – nonparametric density estimation
• Commentaire : 24 pages
• Versions disponibles :  v1 (27-12-2005) v2 (12-06-2006)

• hal-00016328, version 2
• oai:hal.archives-ouvertes.fr:hal-00016328
• Contributeur :
• Soumis le : Lundi 12 Juin 2006, 20:48:47
• Dernière modification le : Lundi 12 Juin 2006, 21:19:41