Eric Barat

Nonparametric bayesian inference in nuclear spectrometry

We address the problem of X/gamma-ray spectra estimation in the fields of nuclear physics. Bayesian estimation of experimental backgrounds has been studied in [1] involving splines. Since Dirichlet processes (DP) sit on discrete measures, they provide an appealing prior for photopeaks. On the other hand, in order to tackle the complexity of experimental backgrounds, we consider a Polya Tree Mixture (PTM) - with suitable parameters yielding distribution continuity - for which predictive densities exhibit better smoothness properties than a single Polya Tree. Furthermore, it is easy to introduce some physical Compton line approximation formula (e.g. Klein-Nishina) in the base measure of the Polya Tree, or some physically driven local modifications of the PTM prior parameters. As backgrounds depend on photopeaks locations, we propose a hierarchical model where the PTM is conditioned on the DP. We use a beta prior for the mixing proportion between the DP and the PTM. Energies are not directly observed due to detection devices noises which introduce a convolution of both discrete and continuous measures by an assumed gaussian kernel whose variance is an unknown linear function of energy. Thus, the proposed semiparametric model for experimental data becomes a hierarchical Polya Tree-Dirichlet mixture of normal kernels. Besides, observed energies are binned in an histogram introducing additional quantification noise. The quantities of interest are usually posterior functionals of the DP mixing distribution. This implies an inverse problem which is carried out in the framework of finite stick-breaking representation. Thanks to conjugacy, draws from the posterior DP and PTM are easily obtained. The approach yields to a global peaks/background separation while offering spectrum resolution enhancement. The method is illustrated on experimental HPGe spectra.

Pile-up correction algorithms for nuclear spectrometry

This article presents a problem encountered in nuclear physics, queuing theory and point processes. The studied signal consists of pulses of random length and energy, possibly sampled, whose time occurrences are points of an homogenous Poisson process. Incoming pulses can combine into pile-ups, which results in a biased estimation of the density of lengths and energies. We introduce a model based on two marked point processes and derive an analytical relation between the probability density function (pdf) of the observed pile-ups and the pdf of the pulses, that leads to an algorithm for pile-up correction, in both continuous time and discrete time signals. Simulations show cancellation of the pile-up effect and prove efficiency of the algorithms in gamma spectrometry.

A nonparametric bayesian approach for PET reconstruction

We introduce a PET reconstruction algorithm following a nonparametric Bayesian (NPB) approach. In contrast with expectation maximization (EM), the proposed technique does not rely on any space discretization. Namely, the activity distribution - normalized emission intensity of the spatial Poisson process - is considered as a spatial probability density and observations are the projections of random emissions whose distribution has to be estimated. This approach is nonparametric in the sense that the quantity of interest belongs to the set of probability measures on Rk (for reconstruction in k-dimensions) and it is Bayesian in the sense that we define a prior directly on this spatial measure and infer on the posterior distribution of the activity distribution. In this context, we propose to model the nonparametric probability density as an infinite mixture of multivariate normal distributions. As a prior for this mixture we consider a Dirichlet process mixture (DPM) with a normal-inverse wishart (NTW) model as base distribution of the Dirichlet process. As in EM-family reconstruction, we use a data augmentation scheme where the set of hidden variables are the emission locations in the continuous object space for each observed coincidence. Thanks to the data augmentation, we propose a Markov chain Monte Carlo (MCMC) algorithm (Gibbs sampler) which is able to generate draws from the posterior distribution of the spatial intensity. A difference with EM is that hidden variables involved in the Gibbs sampler correspond to generated emission locations while the number of emissions per pixel detected on a projection line is used for complete data in EM. Another key difference is that the estimated spatial intensity is a continuous function - such that there is no need to compute a projection matrix - while parameters in EM are given by the mean intensity per pixel. Finally, draws from the intensity posterior distribution allow the estimation of posterior functionals like the mean and variance or confidence intervals. The nonparametric behavior is characterized by an increase of DPM components (clusters) and consequently a resolution improvement with the number of recorded events. Results are presented for simulated data based on a 2D brain phantom and compared to ML-EM and Bayesian MAP-EM.

A discrete-continuous Bayesian model for Emission Tomography

In this contribution, we propose a discrete-continuous reconstruction method for Positron Emission Tomography (PET). The goal is to reconstruct a continuous radiotracer activity distribution from a finite set of measurements (namely, the discrete projections of detected random emissions). Our approach can be viewed as an indirect density estimation problem, i.e, the problem of recovering a probability density function based on indirect observations. We cast the reconstruction problem in a Bayesian nonparametric estimation framework where regularization of the ill-posed inverse problem is achieved by putting a prior on the investigated radiotracer activity distribution. We propose a hierarchical model and use it for the MCMC schemes to generate samples from the posterior activity distribution and compute its functionals (mean, standard deviation etc.). Results will illustrate the performances of the proposed method and we compare our approach to another Bayesian method, the maximum a posteriori estimation (MAP), which is based on a fully discrete-discrete problem formulation.

ADONIS : a new system for high count rate HPGe γ spectrometry

The ADONIS (Algorithmic Development framewOrk for Nuclear Instrumentation and Spectrometry) system is a new γ spectrometer which addresses high count rate metrology. It has been developed for count rate up to 106 cps and beyond on HPGe detectors. The ADONIS system has been designed in order to: (1) maximize the (pile-up free) output count rate (OCR), (2) achieve both qualitative (i.e. Gaussian shape of spectrum peaks) and quantitative (i.e. reliable metrology) spectrometry, and (3) maintain these results even with time-varying activities. The actual instrument is based on a PC, hosting a PCI acquisition board, together with the standalone analog and digital front end module. The system allows data storage on hard disk for eventual off-line signal analysis. One of the main advantage of such a system is that there is no tuning depending on both input count rate (ICR) and charge collection duration. The accuracy of energy estimation naturally decreases as ICR increases. The same performances as conventional systems are reached at low ICR. For the user no trade-off between resolution and throughput has to be made.

Ionizing radiation detection using jump markov linear systems

The systems commonly used to detect photons and estimate their energies are usually irrelevant for high flux. Hidden Markov model and jump Markov linear systems (JMLS) provide a framework which allows us to get an optimal estimate for stochastic processes, whose occurrences are randomly distributed according to time of detection, length and magnitude. It is perfectly adapted to the spectrometry issue. We use the maximum a posteriori (MAP) criterion to estimate the state vector. In the high signal-to-noise ratio (SNR) case, the system can be simplified as a Kalman smoother set up in an on-line version in our lab. An extension in low SNR case is proposed

Gammastic: Towards a pseudo-gamma spectrometry in plastic scintillators

War against CBRN-E threats needs to continuously develop sensors with improved detection efficiency. More particularly, this topic concerns the NR controls for homeland security. A first analysis requires indeed a fast gamma spectrometry so as to detect potential special nuclear materials (SNM). To this aim, plastic scintillators could represent the best alternative for the production of large-scale, low-cost radiation portal monitors to be deployed on boarders, tolls, etc. Although they are known to be highly sensitive to gamma rays, due to their poor resolution, information relative to the nature of the SNM is tricky. Thus, only the Compton edge is obtained after interaction, and no information of the photoelectric peak is observed. This project concerns new developments on a possible pseudogamma spectrometry performed with plastic scintillators. This project is articulated on a combination of two developments: - The design of new materials most suitable for recovering the photoelectric peak after gamma interaction with the scintillator. This work concerns mainly plastic scintillators loading with heavy elements, such as lead or bismuth. - The analysis of the resulting signal with smart algorithms. This work is thus a pluridisciplinary work performed at CEA LIST and embeds 4 main disciplines: MCNPX simulations (simulated spectra), chemistry of materials (preparation of various plastic scintillators with different properties), instrumentation (lab experiments) and smart algorithms. Really impressive results were obtained with the unfolding of simulated spectra at various energies (from 241Am to 60Co) and an innovative approach was proposed to counter-balance the quenching effect of luminescence by heavy elements in plastic scintillators.

Performance of ADONIS-LYNX system for burn-up measurement applications at AREVA NC La Hague reprocessing plant

This work deals with the last measurement campaign done at the AREVA NC La Hague reprocessing plant with the new industrial ADONIS system called ADONIS LYNX. In this paper we briefly explain the ADONIS bimodal Kalman smoother. Next, we present the experimental set-up as well as the industrial approach for the ADONIS system. Results from measurement campaign are then discussed. Some ways of improvement are also explained.

Continuous space-time reconstruction in 4D PET

The aim of this work is to propose a method for reconstructing space-time 4D PET images directly from the data without any discretization, neither in space nor in time. To accomplish this, we cast the reconstruction problem in the context of Bayesian nonparametrics (BNP). The 4D activity distribution is viewed as an entire probability density on ℝ3×ℝ+ and inferred directly. The regularization of the inverse problem is done in the Bayesian framework. We put a prior on the random probability measure of interest and compute its posterior. The random activity distribution is modeled as a dependent Dirichlet process mixture (DPM). By assuming independence between space and time random distributions in each component of the mixture for brain functional imaging, we use a Normal-Inverse Wishart (NIW) model as base distribution for the marginalized spatial Dirichlet process. The time dependency is taken into account through a nested DPM of Pólya Trees. The resulting hierarchical nonparametric model allows inference on the so-called functional volumes which define regions of brain whose activity follows a particular kinetic. A challenging task is to tackle the infinite distributions without truncation of models. We approximate the targeted posterior distribution of the space-time distribution with a Markov Chain Monte-Carlo (MCMC) inference scheme for which we make use of a particular update formula combined with a strategy called slice sampling that allows to deal with a finite number of components at each sweep of the sampler. The Bayesian nature of the proposed method gives access to posterior uncertainty. This ability will be used to explore the behavior of the reconstruction algorithm in a situation of low injected doses. To assess our results in this context, we furnish a statistical validation based on synthetic replicates in 3D. An application to space-time PET reconstruction is presented for simulated data from a 4D digital phantom and preliminary results on real data are provided.

Nonparametric Bayesian Estimation of Censored Counter Intensity from the Indicator Data

The nonparametric Bayesian estimation of non homogeneous Poisson process intensity in presence of Type‐I or Type‐II dead times is addressed in the framework of multiplicative intensity counting processes. In addition to the counting process, the idle/dead time (on/off) process is observed. Inference is based on the partial likelihood either for non‐informative (Type‐I) or for informative censoring (Type‐II). A Polya tree process with suitable partition construction is proposed as nonparametric prior for the normalized multiplicative intensity. Performances are illustrated on both types of censored counters.