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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

• 1:  Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
• http://www.ltci.telecom-paristech.fr/
Télécom ParisTech – CNRS : UMR5141 CNRS LTCI Télécom ParisTech 46 rue Barrault F-75634 Paris Cedex 13 France
• 2:  Laboratoire d'Electronique et de Traitement du Signal (LETS)

• CEA : DRT/DETECS/SSTM/LETS France
• 3:  Hebrew University of Jerusalem (HUJ)
• http://www.huji.ac.il/huji/eng/
Hebrew University of Jerusalem Jerusalem 91905 Israel
• Available versions :  v1 (2005-12-27) v2 (2006-06-12)
• Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject: Mathematics/Statistics
• Title: Nonparametric inference of photon energy distribution from indirect measurements
• Abstract: 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.
• Fulltext language: English
• Keyword(s): indirect observations – marked Poisson processes – nonlinear inverse problems – nonparametric density estimation
• Comment: 24 pages

Attached file list to this document:

 TEX
 Bernoulli_2005.tex(9.3 KB)
 appendix.tex(46.1 KB)
 estimator_detail.tex(27 KB)
 stat_aspects.tex(12.8 KB)
 introduction.tex(7.8 KB)
 Bibliographie.bib(8 KB)
 ims.bst(30.6 KB)
 id_CS137.eps(61.6 KB)
 empilement_CS137.eps(24.6 KB)
 Fig_intro.tex(1.9 KB)
 Fig_intro.eps(16.9 KB)
 desempilement_CS137.eps(20.1 KB)
 FIGURE_DESEMPILEE.eps(14.9 KB)
 applications.tex(7.8 KB)
 FIGURE_EMPILEE.eps(13.4 KB)
 Bernoulli_2005.bbl(3.5 KB)
 FIGURE_DESEMPILEE_NEW.eps(15.1 KB)
 NOTATIONS.tex(5.1 KB)
 Marges.tex(460 B)
 Packages_Eng.tex(1.7 KB)
 PDF
 Bernoulli_2005.pdf(359.6 KB)
 PS
 Bernoulli_2005.ps(365.4 KB)

• hal-00016328, version 2
• oai:hal.archives-ouvertes.fr:hal-00016328
• From:
• Submitted on: Monday, 12 June 2006 20:48:47
• Updated on: Monday, 12 June 2006 21:19:41