Nonparametric inference of photon energy distribution from indirect measurements

International audienceWe 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

Fast Digital Filtering of Spectrometric Data for Pile-up Correction

International audienceThis paper considers a problem stemming from the analysis of spectrometric data. When performing experiments on highly radioactive matter, electrical pulses recorded by the spectrometer tend to overlap, thus yielding severe distortions when computing the histogram of the pulses' energies. In this paper, we propose a fast recursive algorithm which estimates efficiently this histogram from measurements of the duration and energies of overlapping pulses. Its good performances are shown both on simulations and real data. Furthermore, its lower algorithmic complexity makes it more fitting for real-time implementation

New avenues for therapy in mitochondrial optic neuropathies

Mitochondrial optic neuropathies are a group of optic nerve atrophies exemplified by the two commonest conditions in this group, autosomal dominant optic atrophy (ADOA) and Leber’s hereditary optic neuropathy (LHON). Their clinical features comprise reduced visual acuity, colour vision deficits, centro-caecal scotomas and optic disc pallor with thinning of the retinal nerve fibre layer. The primary aetiology is genetic, with underlying nuclear or mitochondrial gene mutations. The primary pathology is owing to retinal ganglion cell dysfunction and degeneration. There is currently only one approved treatment and no curative therapy is available. In this review we summarise the genetic and clinical features of ADOA and LHON and then examine what new avenues there may be for therapeutic intervention. The therapeutic strategies to manage LHON and ADOA can be split into four categories: prevention, compensation, replacement and repair. Prevention is technically an option by modifying risk factors such as smoking cessation, or by utilising pre-implantation genetic diagnosis, although this is unlikely to be applied in mitochondrial optic neuropathies due to the non-life threatening and variable nature of these conditions. Compensation involves pharmacological interventions that ameliorate the mitochondrial dysfunction at a cellular and tissue level. Replacement and repair are exciting new emerging areas. Clinical trials, both published and underway, in this area are likely to reveal future potential benefits, since new therapies are desperately needed

TRAITEMENT STATISTIQUE DU SIGNAL SPECTROMETRIQUE :<br />Etude du désempilement de spectre en énergie pour la spectrométrie gamma

The main objective of spectrometry is to characterize the radioactive elements of an unknown source by studying the energy of the emitted gamma photons. When a photon interacts with a detector,its photonic energy is converted into an electrical pulse, whose integral energy is measured. The histogram obtained by collecting the energies can be used to identify radioactive elements andmeasure their activity.However, at high counting rates, perturbations which are due to the stochastic aspect of the temporal signal can cripple the identification of the radioactive elements. More specifically, since the detector has a finite resolution, close arrival times of photons which can be modeled as an homogeneous Poisson process cause pileups of individual pulses. This phenomenon distorts energy spectra by introducing multiple fake spikes and prolonging artificially the Compton continuum, which can mask spikes of lowintensity.The objective of this thesis is to correct the distortion caused by the pileup phenomenon in the energy spectra. Since the shape of photonic pulses depends on many physical parameters, we considerthis problem in a nonparametric framework. By introducing an adapted model based on two marked point processes, we establish a nonlinear relation between the probability measure associated to the observations and the probability density function we wish to estimate. This relation is derived both for continuous and for discrete time signals, and therefore can be used on a large set of detectors and from an analogical or digital point of view. It also provides a framework to this problem, which can be considered as a problem of nonlinear density deconvolution and nonparametric density estimation from indirect measurements.Using these considerations, we propose an estimator obtained by direct inversion. We show that this estimator is consistent and almost achieves the usual rate of convergence obtained in classicalnonparametric density estimation in the L2 sense. We illustrate these theoretical aspects of our study with numerical results obtained both on simulations and on energy spectra associated to real-world data from the ADONIS intrumentation systemdeveloped by the CEA Saclay. We show that the distortions caused by the pileup phenomenon are well corrected by the algorithms derived from our estimators.Dans le cadre de la spectrométrie Gamma, on s'intéresse à la caractérisation des éléments radioactifs d'une source à partir des photons gamma émis par cette dernière. A des taux de comptage élevés, des perturbations liées à l'aspect stochastique du signal étudié sont susceptibles de gêner l'identification des éléments radioactifs. En particulier, les arrivées aléatoires des photons sont susceptibles de produire des empilements. Ce phénomène introduit une distortion du spectre en énergie, notamment l'apparition de faux pics multiples et une distortion du continuum Compton qui peut masquer des pics de faible intensité.L'objectif de cette étude est de corriger les distortions des spectres en énergie causées par les empilements d'impulsions photoniques. Nous nous plaçons pour cela dans un cadre non-paramétrique ; nous établissons une relation non-linéaire entre la loi des observations et la densité de probabilité que l'on cherche à estimer. Elle permet de considérer ce problème dans le cadre de la déconvolution non-linéaire de densités et de l'estimation non-paramétrique à partir de mesures indirectes.A partir de cette relation, nous proposons un estimateur obtenu par inversion directe. Nous montrons que cet estimateur est consistant et que sa vitesse de convergence au sens de la norme L2 est proche des vitesses non-paramétriques usuelles.Nous illustrons ces aspects par des résultats numériques obtenus sur des simulations et des spectres en énergie obtenus à partir du système ADONIS développé par le CEA Saclay. Nous montrons que les distortions dues aux empilements d'impulsions photoniques sont bien corrigées par les algorithmes dérivant de nos estimateurs

Traitement statistique du signal spectrométrique (étude du désempilement de spectre en énergie pour la spectrométrie gamma)

Dans le cadre de la spectrométrie Gamma, on s'intéresse à la caractérisation des éléments radioactifs d'une source à partir des photons gamma émis par cette dernière. A des taux de comptage élevés, des perturbations liées à l'aspect stochastique du signal étudié sont susceptibles de gêner l'identification des éléments radioactifs. En particulier, les arrivées aléatoires des photons sont susceptibles de produire des empilements. Ce phénomène introduit une distortion du spectre en énergie, notamment l'apparition de faux pics multiples et une distortion du continuum Compton qui peut masquer des pics de faible intensité. L'objectif de cette étude est de corriger les distortions des spectres en énergie causées par les empilements d'impulsions photoniques. Nous nous plaçons pour cela dans un cadre non-paramétrique ; nous établissons une relation non-linéaire entre la loi des observations et la densité de probabilité que l'on cherche à estimer. Elle permet de considérer ce problème dans le cadre de la déconvolution non-linéaire de densités et de l'estimation non-paramétrique à partir de mesures indirectes. A partir de cette relation, nous proposons un estimateur obtenu par inversion directe. Nous montrons que cet estimateur est consistant et que sa vitesse de convergence au sens de la norme L2 est proche des vitesses non-paramétriques usuelles. Nous illustrons ces aspects par des résultats numériques obtenus sur des simulations et des spectres en énergie obtenus à partir du système ADONIS développé par le CEA Saclay. Nous montrons que les distortions dues aux empilements d'impulsions photoniques sont bien corrigées par les algorithmes dérivant de nos estimateurs.In Gamma spectrometry, we characterize the radioactive elements of an unknown source by studying the energy of the emitted Gamma photons. At high counting rates, due to the stochastic aspect of the signal, the pileup phenomenon can cripple the identification of the radioactive elements. Specifically, close arrival times of photons which can be modeled as an homogeneous Poisson process cause a distortion of the energy spectra by introducing multiple fake spikes and prolonging artificially the Compton continuum, which can mask spikes of low intensity. The objective of this study is to correct the distortion caused by the pileup phenomenon in the energy spectra. We consider this problem in a nonparametric framework. Using a model based on two marked point processes, we establish a nonlinear relation between the probability measure associated to the observations and the probability density function we wish to estimate. This relation provides a framework to this problem, which can be considered as a problem of nonlinear density deconvolution and nonparametric density estimation from indirect measurements. Using these considerations, we propose an estimator obtained by direct inversion. We show that this estimator is consistent and almost achieves the usual rate of convergence obtained in classical nonparametric density estimation in the L2 sense. We illustrate these aspects by numerical results obtained both on simulations and on energy spectra associated to real-world data from the ADONIS intrumentation system developed by the CEA Saclay. We show that the distortions caused by the pileup phenomenon are well corrected by the algorithms derived from our estimators.PARIS-Télécom ParisTech (751132302) / SudocSudocFranceF