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International audience; We continue studies of the uncertainty quantification problem in emission tomographies such aspositron emission tomography (PET) or single photon emission computed tomography (SPECT)when additional multimodal data (anatomical magnetic resonance imaging (MRI) images) are avail-able. To solve the aforementioned problem we adapt the recently proposed nonparametric posteriorlearning technique to the context of Poisson-type data in emission tomography. Using this approachwe derive sampling algorithms which are trivially parallelizable, scalable and very easy to implement.In addition, we prove conditional consistency and tightness for the distribution of produced samplesin the small noise limit (i.e., when the acquisition time tends to infinity) and derive new geometricaland necessary condition on how MRI images must be used. This condition arises naturally in thecontext of identifiability problem for misspecified generalized Poisson models with wrong design. Wealso contrast our approach with Bayesian Markov chain Monte Carlo sampling based on one dataaugmentation scheme which is very popular in the context of expectation-maximization algorithmsfor PET or SPECT. We show theoretically and also numerically that such data augmentation sig-nificantly increases mixing times for the Markov chain. In view of this, our algorithms seem to givea reasonable trade-off between design complexity, scalability, numerical load and assessment for theuncertainty

The uncertainty of reconstructed PET images remains difficult to assess and to interpret for the use in diagnostic and quantification tasks. Here we provide (1) an easy-to-use methodology for uncertainty assessment for almost any Bayesian model in PET reconstruction from single datasets and (2) a detailed analysis and interpretation of produced posterior image distributions. We apply a recent posterior bootstrap framework to the PET image reconstruction inverse problem and obtain simple parallelizable algorithms based on random weights and on existing maximum a posteriori (MAP) (posterior maximum) optimization-based algorithms. Posterior distributions are produced, analyzed and interpreted for several common Bayesian models. Their relationship with the distribution of the MAP image estimate over multiple dataset realizations is exposed. The coverage properties of posterior distributions are validated. More insight is obtained for the interpretation of posterior distributions in order to open the way for including uncertainty information into diagnostic and quantification tasks.

International audience; In this article, we aim at measuring a low-activity uranium contamination deposited on concrete surfaces of a nuclear facility and presenting varying enrichment levels. Considering this application field, CEA LIST, has developed an original approach, combining gamma-ray spectrometry based on high-purity germanium (HPGe) measurements and specific Bayesian algorithms. This methodology gives access to an indirect surface activity estimation, assuming that the ratio between the number of alpha particles to be quantified and the number of detected gamma rays is known. The Bayesian approach characteristic property is able to inject a representation of the physical context in the form of a probabilistic a priori. It enables to improve the tradeoff between the true detection rate (TDR) and the false alarm rate (FAR) at low count rates and takes benefit of a richer time-energy information structure than the algorithms used in the conventional detection procedures. The performance evaluation and characterization of Bayesian statistical tests are performed using classical receiver-operating characteristic (ROC) curves by comparison to frequentist hypothesis tests. Results indicate that the Bayesian approach has a superior detection performance for low-activity uranium contamination compared to the frequentist approach. The estimated gain is contained between 30% and 50%, considering a variable or stable radiological background. The Bayesian approach offers the best tradeoff between the TDR, FAR, and the response time and is compatible with the user's requirements.

International audience; Nuclear decommissioning takes places after dismantling, and consists of studying the possible presence of any residual contamination. To do so, every surface inside the facility must be radiologically characterized, and every contamination removed. In the case of an alpha contamination linked with a low gamma activity, using a High-Purity Germanium detector (HPGe) combined with hypothesis tests on the count statistics can be helpful to assess said contamination. Gamma-ray activity enables to determine the total contamination activity provided both are related, like in the case of an uranium-based contamination. Hypothesis tests determine the statistical power of the measurement, allowing decision making when dealing with countings below the detection limit. A representation of the tests results using Receiver Operating Characteristics (ROC) curves allow the user to select an appropriate time of measurement, true detection and false alarm rates, in accordance to the required specifications. This paper presents the feasibility study of such a method, applied to the detection of a low-activity gamma surface contamination of uranium on concrete, with varying enrichment levels.

International audience; Radionuclide identification and quantification are a serious concern for many applications as for in situ monitoring at nuclear facilities, laboratory analysis, special nuclear materials detection, environmental monitoring, and waste measurements. High resolution gamma-ray spectrometry based on high purity germanium diode detectors is the best solution available for isotopic identification. Over the last decades, methods have been developed to improve gamma spectra analysis. However, some difficulties remain in the analysis when full energy peaks are folded together with high ratio between their amplitudes, and when the Compton background is much larger compared to the signal of a single peak. In this context, this study deals with the comparison between a conventional analysis based on “iterative peak fitting deconvolution” method and a “nonparametric Bayesian deconvolution” approach developed by the CEA LIST and implemented into the SINBAD code. The iterative peak fit deconvolution is used in this study as a reference method largely validated by industrial standards to unfold complex spectra from HPGe detectors. Complex cases of spectra are studied from IAEA benchmark protocol tests and with measured spectra. The SINBAD code shows promising deconvolution capabilities compared to the conventional method without any expert parameter fine tuning.

International audience; This work aims at developing a generic virtual source model (VSM) preserving all existing correlations between variables stored in a Monte Carlo pre-computed phase space (PS) file, for dose calculation and high-resolution portal image prediction. The reference PS file was calculated using the PENELOPE code, after the flattening filter (FF) of an Elekta Synergy 6 MV photon beam. Each particle was represented in a mobile coordinate system by its radial position (r(s)) in the PS plane, its energy (E), and its polar and azimuthal angles (phi(d) and theta(d)), describing the particle deviation compared to its initial direction after bremsstrahlung, and the deviation orientation. Three sub-sources were created by sorting out particles according to their last interaction location (target, primary collimator or FF). For each sub-source, 4D correlated-histograms were built by storing E, r(s), phi(d) and theta(d) values. Five different adaptive binning schemes were studied to construct 4D histograms of the VSMs, to ensure histogram efficient handling as well as an accurate reproduction of E, r(s), phi(d) and theta(d) distribution details. The five resulting VSMs were then implemented in PENELOPE. Their accuracy was first assessed in the PS plane, by comparing E, r(s), phi(d) and theta(d) distributions with those obtained from the reference PS file. Second, dose distributions computed in water, using the VSMs and the reference PS file located below the FF, and also after collimation in both water and heterogeneous phantom, were compared using a 1.5%-0 mm and a 2%-0 mm global gamma index, respectively. Finally, portal images were calculated without and with phantoms in the beam. The model was then evaluated using a 1%-0 mm global gamma index. Performance of a mono-source VSM was also investigated and led, as with the multi-source model, to excellent results when combined with an adaptive binning scheme.

Conference of 4th International Conference on Advancements in Nuclear Instrumentation Measurement Methods and their Applications, ANIMMA 2015 ; Conference Code:121554; International audience; Radionuclide identification and quantification is a serious concern for many applications as safety or security of nuclear power plant or fuel cycle facility, CBRN risk identification, environmental radioprotection and waste measurements. High resolution gamma-ray spectrometry based on HPGe detectors is a performing solution for all these topics. During last decades, a great number of software has been developed to improve gamma spectra analysis. However, some difficulties remain in the analysis when full energy peaks are folded together with a high ratio between their amplitudes, when the Compton background is much larger compared to the signal of a single peak and when spectra are composed of a great number of peaks. This study deals with the comparison between a conventional analysis method and an innovative approach, called SINBAD ("Spectrométrie par Inférence Non paramétrique BAyesienne Déconvolutive"), for radionuclide identification and quantification. For many years, SINBAD has been developed by the CEA LIST for unfolding complex spectra from HPGe detectors. Contrary to the conventional method using fitting procedures, SINBAD uses a probabilistic approach with nonparametric Bayesian inference to process spectrum data. The conventional fitting method founded for instance in Genie 2000 is compared with the nonparametric SINBAD approach regarding some key figures of merit as the peak centroid estimation (identification step) and net peak area determination (quantification step). Complex cases are studied for nuclide detection with closed gamma-rays energies and high full energy peak intensity differences. Tests are performed with spectra from the International Atomic Energy Agency (IAEA) for gamma spectra analysis software benchmark and with spectra acquired in our laboratory. It appears that SINBAD results are better than GENIE 2000 ones in most of the cases even if hard deconvolutions can be achieved thanks to GENIE 2000 at the cost of expert parameters fine tuning which has to be compared with the user-friendly SINBAD operating.

International audience; This 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.

International audience; Purpose/Objective: Historically designed as a control system for patient positioning for radiotherapy treatment, Electronic Portal Imaging Devices (EPIDs) are nowadays widely used for quality assurance and dosimetric verifications in new irradiation techniques. One of the main advantages of the EPID is its high resolution which can detect small details. The objective of this study is to compare the EPID image acquired during the treatment with a predicted high resolution portal image computed by Monte Carlo (MC) simulation. A new method for prediction of high resolution EPID images is tested for in vivo treatment verification. Materials and Methods: Experiments were carried out on a Siemens ARTISTETM, equipped with a 160-MLCTM, and its Siemens OptivueTM 1000 EPID. This EPID has an active detection area of 41 x 41 cm2 and a matrix of 1024 x 1024 pixels. A model of this linac and the EPID was developed with the MC code Penelope, and commissioned. We focus on a breast treatment conformational beam (6 MV) on the CIRS adult female phantom. The CT-scan of the phantom was used as input, and Hounsfield numbers were converted in density and atomic composition, so as to obtain a voxelized geometry used in the Penelope code. Particles exiting the phantom and impinging on the EPID are simulated up to the EPID in order to compute the predicted portal image by scoring the energy deposited in the phosphor layer on a 1024 x 1024 virtual grid. The simulated image was then smoothed using a denoising algorithm in order to keep the high resolution advantage. Several denoising algorithms were tested, among them IRON, LASG and a recently developed one called DPGLM. For now, we use the gamma-index technique to evaluate the accuracy of the simulated image against the experimental one. Results: Figure 1 shows the acquired image and the simulated one. The gamma-index is satisfied for 94.4 % of the pixels for 3.5 % and 3.5 mm criterion. The DPGLM gives the best result toward accuracy and computed time. Indeed, the denoising of 1024 x 1024 images takes about 1h30 mn, 2h and 5 mn using DPGLM, IRON, and LASG, respectively. The LASG algorithm is really fast but the result is too smoothed for the high resolution purpose. Conclusions: This work is the first step in the aim of in vivo dosimetry by comparing experimental portal images with high resolution predicted images obtained using MC simulations in a voxelized geometry. First results obtained on a breast treatment are encouraging, and we can expect to detect treatment errors.

Purpose/Objective: Electronic Portal Imaging Devices (EPIDs) are widely used for quality assurance in radiotherapy, and also for dosimetric verifications. For this latter application, the image obtained during the treatment session can be compared to a pre-calculated reference image in order to highlight dose delivery errors. A Monte Carlo(MC)-based method to predict high-resolution reference images was recently developed. However, the use of this method in clinical routine is still hampered by the need to store huge phase space (PS) files. This study aims at developing a new virtual source model (VSM) which retains all the existing correlations between particle characteristics stored in the PS file, and hence to provide a more compact way to model the irradiation beam, while keeping the accuracy of using a PS file. Materials and Methods: A model of the studied linac (Elekta Synergy) was first developed using both the MC codes EGSnrc and PENELOPE, and commissioned. Using this model, a reference PSF (PSFr) was calculated after the flattening filter using EGSnrc, where the axial symmetries assumed, and particles were sorted out in three sub-sources according to the position of their last interaction (target, primary collimator or flattening filter). Each particle is described by its radial position (r) in the PS plane,its energy (E), and its polar and azimuthal angles (phi, theta), representing the particle deviation compared to its direction after bremsstrahlung, and the orientation of this deviation. For each subsource, a 4D histogram was built by storing the particle distributions accordingto their r, E, phi, theta values. Our VSM hence contains all correlations existing between these four variables contrary to other existing VSMs. This new VSM is now being implemented in the PENELOPE code, and its accuracy is being tested by comparing first the PSF build using our VSM with the PSFr, and then dose distributions in water and portal images calculated with the MSV and PSFr. Results: Figure 1 shows for each sub-source the correlated 2D histogram depicting particle energy against their radial position. Some characteristics are shared by all sources. Few particles are beyond the collimator aperture (4.5 cm from the linac axis). The annihilation photons at 511 keV are always visible. However, the content of a histogram depends widely of the sub-source it represents: the target produces the most energetic particles. The flattening filter and the primary collimator sub-sources generate particles beyond 4.5 cm of lower energy, because of their large deflection angle. Conclusions: A new VSM taking into account for all correlations between particle characteristics was developed and implemented in the PENELOPE code. It will be used to calculate accurate reference portal images for quality assurance in radiotherapy.

International audience; This article presents the synthesis and the blend of bismuth complexes in polystyrene based plastic scintillators. A specific design has enabled the fabrication of a scintillator loaded with up to 17 wt% of bismuth. Tri-carboxylate and triaryl bismuth compounds were used to explore and understand the influence of bismuth loading on the two main criteria of plastic scintillation: light yield and detection efficiency of gamma-rays. For gamma radiation with an energy

We address the problem of nuclear spectrometry when input count rates are high enough that, in order to limit pile up, classical processing (shaping filter) differs drastically from matched filter solution. We propose a new representation of radiation signals based on a bimodal state space model which leads to a breakthrough in quantitative analysis for high particles rates.

International audience; We propose a nonparametric and Bayesian method for reconstructing dynamic Positron Emission Tomography (PET) images from clinical data. PET is a nuclear medicine imaging modality that uses molecules labeled with a positron emitting radionuclide. It is then possible to image in vivo molecular interactions of biological processes. Our approach is non-parametric in the sense that the image representing the 4D (3D+t) activity distribution is viewed as a probability density on R 3 × R + and inferred directly from the data, without any prior space or time discretization. Being nonparametric, we do not pre-assume any particular functional form for this space-time distribution. Formulating the nonparametric problem in the Bayesian framework allows to characterize the entire 4D distribution of the unknown. Furthermore, this framework allows to access directly to the reconstruction error. The ability of the proposed model is assessed using data from clinical studies and we evaluate its performance against the conventional independent time-frame reconstruction approach using the maximum likelihood algorithm (ML-EM).

Conference of 2013 3rd International Conference on Advancements in Nuclear Instrumentation, Measurement Methods and Their Applications, ANIMMA 2013 ; Conference Date: 23 June 2013 Through 27 June 2013; Conference Code:102802; International audience; 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.

Conference of 2013 3rd International Conference on Advancements in Nuclear Instrumentation, Measurement Methods and Their Applications, ANIMMA 2013 ; Conference Code:102802; International audience; 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 pseudo-gamma 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.

International audience; This work investigates the possibility of combining Monte Carlo (MC) simulations to a denoising algorithm for the accurate prediction of images acquired using amorphous silicon (a-Si) electronic portal imaging devices (EPIDs). An accurate MC model of the Siemens OptiVue1000 EPID was first developed using the penelope code, integrating a non-uniform backscatter modelling. Two already existing denoising algorithms were then applied on simulated portal images, namely the iterative reduction of noise (IRON) method and the locally adaptive Savitzky–Golay (LASG) method. A third denoising method, based on a nonparametric Bayesian framework and called DPGLM (for Dirichlet process generalized linear model) was also developed. Performances of the IRON, LASG and DPGLM methods, in terms of smoothing capabilities and computation time, were compared for portal images computed for different values of the RMS pixel noise (up to 10%) in three different configurations, a heterogeneous phantom irradiated by a non-conformal 15 × 15 cm$^2$ field, a conformal beam from a pelvis treatment plan, and an IMRT beam from a prostate treatment plan. For all configurations, DPGLM outperforms both IRON and LASG by providing better smoothing performances and demonstrating a better robustness with respect to noise. Additionally, no parameter tuning is required by DPGLM, which makes the denoising step very generic and easy to handle for any portal image. Concerning the computation time, the denoising of 1024 × 1024 images takes about 1 h 30 min, 2 h and 5 min using DPGLM, IRON, and LASG, respectively. This paper shows the feasibility to predict within a few hours and with the same resolution as real images accurate portal images, combining MC simulations with the DPGLM denoising algorithm.

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 Polya 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.

ADONIS is a digital system for gamma-ray spectrometry, developed by CEA. This system achieves high count-rate gamma-ray spectrometry with correct dynamic dead-time correction, up to, at least, more than an incoming count rate of 3.106 events per second. An application of such a system at AREVA NC's La Hague plant is the irradiated fuel scanning facility before reprocessing. The ADONIS system is presented, then the measurement set-up and, last, the measurement results with reference measurements.

Previous works on pressurized water reactors show that the nitrogen 16 activation product can be used to measure thermal power. Power monitoring using a more stable indicator than ex-core neutron measurements is required for operational sodium-cooled fast reactors, in order to improve their economic efficiency at the nominal operating point. The fluorine 20 and neon 23 produced by (n,α) and (n,p) capture in the sodium coolant have this type of convenient characteristic, suitable for power measurements with low build-up effects and a potentially limited temperature, flow rate, burn-up and breeding dependence. This method was tested for the first time during the final tests program of the French Phénix sodium-cooled fast reactor at CEA Marcoule, using the ADONIS gamma pulse analyzer. Despite a non-optimal experimental configuration for this application, the delayed gamma power measurement was pre-validated, and found to provide promising results.

This work deals with the use of gamma spectrometry for fourth generation Sodium Fast Reactor (SFR) power monitoring and clad failure detection. Usually, gamma spectrometers could not manage on-line applications in high count rate and fast activity variations but recent improvements in this research field may improve it. The ADONIS analyser for gamma spectrometry could met two needs of fourth generation SFR [1]. The ex-core neutron power measurement gives instant neutron power estimation but has some shift problems, mainly due to the burn-up phenomenon. High security margins are then set and so, the reactor can not work at its best thermodynamic efficiency. Previous works on Pressurized Water Reactors (PWR) show that gamma emitters concentration in primary coolant is also directly linked with reactor power (16N power measurement) [7]. On SFR, the use of short decay period gamma emitters as the 20F radionuclide will allow a fast power measurement with a direct correlation with the instant fission rate and without burn-up dependency. The second need is the clad failure detection improvement. The SFR clad failure detection is done by radiochemical and gamma measurements on argon cover gas and primary sodium samples. Gaseous fission products and delayed neutron fission products (only the 137I and the 87Br) are measured but lots of fission products (gamma emitters) are not measured nowadays on-line due to high sodium activity and its fast changes. This paper presents the experiment done at the French Phenix SFR of the CEA Marcoule and its analysis. Measuring activation and fission products contained in primary sodium coolant, the adaptive ADONIS gamma spectrometry system set on primary sodium coolant sample could be a new innovating power monitoring and clad failure detection system for future SFR.

This work deals with the use of gamma spectrometry to monitor the fourth generation sodium fast reactor (SFR) power. Simulation part has shown that power monitoring in short response time and with high accuracy is possible measuring delayed gamma emitters produced in the liquid sodium. An experimental test is under preparation at French SFR Phenix experimental reactor to validate simulation studies.

Sodium Fast Reactors (SFR) are studied in the international generation IV project to preserve uranium resources and transmute minor actinides. The french Phenix experimental reactor has already shown promising results. The reactor power is commonly calculated simultaneously by heat balance on water to vapour heat exchanger and by neutron flux measurements. Concentration of some gamma radionuclides in the primary coolant is also directly correlated with power. Therefore, we think that an on-line gamma measurement system could be settled as another help for generation IV SFR reactor exploitation. The 20F is a particularly convenient tagging agent to design a fast time response system. This work shows that a gamma spectrometry system measuring the 20F activity could be set as a power monitoring system for SFR reactor. This system will be tested at the Phenix reactor with the high count rate and high resolution Adonis spectrometer.

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.

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. 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 (NIW) model as base distribution of the Dirichlet Process. As in EM‐family reconstr...

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.

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.

The thermal neutron radiative capture cross section for the K isomeric state in {sup 177}Lu has been measured for the first time. Several {sup 177}Lu{sup m} targets have been prepared and irradiated in various neutron fluxes at the Lauee Langevin Institute in Grenoble and at the CEA reactors OSIRIS and ORPHEE in Saclay. The method consists of measuring the {sup 178}Lu activity by {gamma}-ray spectroscopy. The values obtained in four different neutron spectra have been used to calculate the resonance integral of the radiative capture cross section for {sup 177}Lu{sup m}. In addition, an indirect method leads to the determination of the {sup 177}Lu{sup g} neutron radiative capture cross section.

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.

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.

The nonparametric Bayesian estimation of physical spectra is addressed by considering a mixture involving a Dirichlet process in order to capture the hidden discrete nature of peaks and a Polya tree to tackle the complexity of the hidden continuous background.

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.