Nonparametric estimation of a shot-noise process

Paul Ilhe (1) , François Roueff (1) , Éric Moulines (2, 3) , Antoine Souloumiac (4)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 XPOP - Modélisation en pharmacologie de population
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 LADIS (CEA, LIST) - Laboratoire d'analyse des données et d'intelligence des systèmes (CEA, LIST)

We propose an efficient method to estimate in a nonpara-metric fashion the marks' density of a shot-noise process in presence of pile-up from a sample of low-frequency observations. Based on a functional equation linking the marks' density to the characteristic function of the observations and its derivative, we propose a new time-efficient method using B-splines to estimate the density of the underlying γ-ray spectrum which is able to handle large datasets used in nuclear physics. A discussion on the numerical computation of the algorithm and its performances on simulated data are provided to support our findings.

Mots clés: pile-up correction; γ-spectroscopy; B- splines; nonparametric estimation; Shot-noise; Estimation; Photonics; Detectors; Signal processing algorithms; functional equations; gamma-ray spectroscopy; high energy physics instrumentation computing; functional equation; time-efficient method; B-splines; gamma-ray spectrum; nuclear physics; Index Terms-Shot-noise

Domaines: Traitement du signal et de l'image [eess.SP]; Physique Nucléaire Expérimentale [nucl-ex]; Méthodologie [stat.ME]; Analyse de données, Statistiques et Probabilités [physics.data-an]

Paul Ilhe, François Roueff, Éric Moulines, Antoine Souloumiac. Nonparametric estimation of a shot-noise process. SSP 16 - Statistical Signal Processing Workshop, IEEE Signal Processing Society, Jun 2016, Palma de Mallorca, Spain. pp.7551709, ⟨10.1109/SSP.2016.7551709⟩. ⟨hal-01418963⟩