Expectation-propagation for weak radionuclide identification at radiation portal monitors.

We propose a sparsity-promoting Bayesian algorithm capable of identifying radionuclide signatures from weak sources in the presence of a high radiation background. The proposed method is relevant to radiation identification for security applications. In such scenarios, the background typically consists of terrestrial, cosmic, and cosmogenic radiation that may cause false positive responses. We evaluate the new Bayesian approach using gamma-ray data and are able to identify weapons-grade plutonium, masked by naturally-occurring radioactive material (NORM), in a measurement time of a few seconds. We demonstrate this identification capability using organic scintillators (stilbene crystals and EJ-309 liquid scintillators), which do not provide direct, high-resolution, source spectroscopic information. Compared to the EJ-309 detector, the stilbene-based detector exhibits a lower identification error, on average, owing to its better energy resolution. Organic scintillators are used within radiation portal monitors to detect gamma rays emitted from conveyances crossing ports of entry. The described method is therefore applicable to radiation portal monitors deployed in the field and could improve their threat discrimination capability by minimizing “nuisance” alarms produced either by NORM-bearing materials found in shipped cargoes, such as ceramics and fertilizers, or radionuclides in recently treated nuclear medicine patients.

Border protection agents screen inbound vehicles and cargo containers for suspicious levels of radiation relative to the background, and flag these for a more thorough secondary inspection. Detecting smuggled nuclear and radiological material is analogous to finding a needle in a haystack, whereby SNMs can be difficult to detect, quantify, and locate. Nuisance alarms are radiation alarms caused by sources of radiation that pose no security threat. Many common goods shipped across border crossings contain sufficient naturally occurring radioactive material (NORM) to set off gamma alarms in RPMs 4 . Medical isotopes are another growing source of nuisance alarms. A patient may emit sufficient gamma radiation for days or even weeks after a procedure to set off an RPM gamma alarm [4][5][6][7] , depending on the nuclear medicine isotope used and its administered activity.
NORM-bearing cargo and nuclear medicine patients are significantly more prevalent than nuclear smugglers in cross-border traffic. Hence, customs and border protection agents spend an exorbitant amount of time processing nuisance alarms in secondary inspections that can last tens of minutes per offending vehicle or cargo container 8 . Due to the low signal to background ratio, simply alarming on the presence of a radioactive source is a challenge in itself for primary inspection. In the interest of saving time for both customs and border protection agents, as well as people crossing borders, combining primary and secondary inspections appears as an attractive solution. In an ideal scenario, the primary inspection would simultaneously detect, identify and quantify any source of radiation of interest, so that, for example, nuclear medicine patients avoid the discomfort caused by a lengthy secondary inspection. Identifying radionuclides, however, is even more sensitive to signal-to-background ratio than simply detecting the presence of a radiation source.
One concerning and challenging scenario involves the contextual presence of multiple radionuclides, i.e., mixed sources. In this case, strong NORM sources can mask a weaker SNM source, and further jeopardize the identification process. Gamma-ray spectroscopy inspections performed using inorganic scintillators or semiconductor detectors, such as NaI(Tl) or HPGe, respectively, are typically able to resolve most of the photopeaks, which serve as fingerprints of the present radionuclides, and therefore facilitate the nuclide identification in a mixed source scenario 9 . The vast majority of deployed RPMs utilizes instead organic scintillators, i.e., PVT, because of the high intrinsic efficiency of these detectors, their relatively low cost, and suitability to be produced in large shapes. The response of organic scintillator-based RPMs is not characterized by sharp photopeaks, but rather by smooth edges and continuum regions that result from Compton scattering interactions. Therefore, the spectral response of an RPM organic scintillator to a mixed source will essentially be a smooth linear combination of the responses to individual sources. It is hence challenging to identify all the components of the mixed source and estimate the relative activities of the constituent sources.
The performance of a portal monitor in terms of sensitivity, i.e., maximization of the positive detection rate, is a function of the detection efficiency of the system and its form factor, which should be optimized for a specific application. Paff and colleagues 8 have already shown that the system sensitivity can be optimized by selecting large detector panels. In this work, we focus on the capability of identifying multiple sources in a mixture of nuclides, following an alarm event.
The proposed method is also relevant to a number of other radiation identification and localization applications, such as radionuclide search with unmanned vehicles in a given environment, where the statistics of the signal of interest is poor compared to the background, because of short measurement time, distance between the detector and the source, low detection intrinsic efficiency and/or weakness of the source.

Algorithms for RpM signal unmixing
Radiation detection and characterization in the nuclear security area is challenging due to the low intensity of the signal of interest, typically much lower than the background. Two main detrimental components are added to the SNM signal of interest: spectra of additional NORM sources, either located inside the cargo or part of the natural background surrounding the portal monitor, and intrinsic observation Poisson noise (shot noise), which is not negligible for short measurement times and therefore can lead to poor signal-to-noise ratios. Bayesian inference is particularly attractive in such challenging scenarios, and advances in approximate methods 10,11 allow complex models to be used with computational times compatible with real-time constraints.
Bayesian approaches to detect, classify, and estimate smuggled nuclear and radiological materials are not a new consideration 6,12 , and were extensively studied for the development of the Statistical Radiation Detection System at Lawrence Livermore National Laboratory. This group has used Bayesian model-based sequential statistical processing techniques to overcome the low signal-to-background ratio that complicates traditional gamma spectroscopy techniques with high-resolution HPGe and inorganic scintillation detectors 13,14 . Bayesian approaches have also been applied to radionuclide identification for NaI(Tl) detectors using a wavelet-based peak identification algorithm with Bayesian classifiers 15 , for LaBr 3 (Ce) using a sequential approach 16 , and to HPGe detectors using non-parametric Bayesian deconvolution to resolve overlapping peaks 17 . Bayesian approaches have been recently investigated for the detection of single and mixed gamma sources with short measurement times 12 . The use of related machine-learning-based methods was also recently demonstrated for source identification in spectra recorded using inorganic scintillators 18 .

Results
In this study, we considered two types of organic scintillation detectors, based on liquid EJ-309 and stilbene crystal, respectively, as detailed in the "Methods" section. The functional difference between the two detectors most relevant to this work is their energy resolution as illustrated in Fig. 1, which depicts their integral-normalized response to a 201 Tl (left) and to a 99m Tc (right) source. This figure shows that stilbene exhibits sharper Compton edges than EJ-309, thanks to its better energy resolution. Table 1 lists the 11 nuclides that were measured using the two different detectors, and the relative fractions used to generate synthetic mixtures and assess the performance of the new algorithm. For each mixture, several data sets were created to obtain spectra with a total counts from 500 to 500 k, where the observation noise was modeled by Poisson noise.
We compared the unmixing performance of the new algorithm, referred to as MMSE BTG , to that of two Bayesian strategies, namely the maximum a-posteriori (MAP) and the minimum mean squared error (MMSE L1 ) approaches presented in 12 . These two approaches, denoted by MAP L1 and MMSE L1 , respectively, are detailed in the "Methods" section.
As the metric for estimation accuracy, we used the root-mean-square error (RMSE) between the known nuclide fractions z and their estimated values ẑ, where N is the number of nuclides in the spectral library. Figure 2 compares the RMSEs obtained by the three methods mentioned above for the nine mixtures of Table 1, as the total number of counts increases (from 500 to 1 M) and using the stilbene detector. The new MMSE BTG method generally provides more robust results, compared to the MAP L1 and MMSE L1 approaches, yielding consistently lower RMSEs. The MMSE BTG RMSE becomes comparable to the MAP L1 RMSE when only 500 counts are measured, and when the mixture contains nuclides with spectral similarities, e.g., 123 I and 99m Tc in the fourth mixture. The RMSEs obtained using the MMSE BTG algorithm and simulated data show overall comparable performances using either detector (see Fig. 3). The results using the stilbene detector are slightly better, i.e., present lower RMSEs, especially for mixtures of three or more nuclides, e.g., WGPu, 99m Tc, and 67 Ga (mixture 3). This result is expected because of the better energy resolution of stilbene, compared to EJ-309. Similar results have been obtained with the two other competing methods.  Table 1. Composition of the nine mixtures tested in this work. The fractions represent the ratio of the detected counts associated with each source.
A significant advantage of the proposed MMSE BTG algorithm is that it directly provides uncertainty quantification, i.e., the estimated probability of the presence of each source from the library. The MMSE BTG algorithm generates theses estimates from the posterior distribution, which are not directly available from the MAP L1 and  Table 1 and measured with the stilbene detector, as a function of the detection counts. www.nature.com/scientificreports www.nature.com/scientificreports/ MMSE L1 algorithms. If the measured spectrum consists of more than 1000 counts, the algorithm correctly identifies with high probability the nuclides in the mixture and its performance slightly degrades as the number of sources that are present increases and the overall gamma counts per source decrease (see Fig. 4). In addition to providing estimated probabilities of source presence, the MMSE BTG yields superior performance, compared to the MAP L1 and MMSE L1 algorithms used in Fig. 2. Furthermore, in contrast to the proposed MMSE BTG approach, the MMSE L1 and MAP L1 algorithms require tuning of a threshold for source detection, whose optimal value (in terms of probabilities of false alarm and detection) is difficult to tune in practice, as it depends on the counts and the mixture composition. For this reason, we only report here the detection results obtained using the MMSE BTG approach.
In Fig. 4, an increasing number of isotopes not present in the actual mixture is identified as potentially present, when there are few gamma counts. For example, for sparse spectra (<1,000 counts) containing WGPu and 99m Tc (mixtures 6-9), the algorithm suggests the potential presence of 123 I. This can be explained by the similarity of the spectra of 123 I and 99m Tc (as shown in Fig. 5). The discrimination of these two nuclides becomes easier as the gamma counts increase.
Mixtures 6-9 simulate a specific scenario, where a WGPu source is detected together with an increasing amount of 99m Tc, which is the most commonly used medical radioisotope and could, therefore, be used to mask (in terms of relative counts) the presence of WGPu. The results illustrate that the estimated probability of presence of WGPu decreases as its proportion decreases in the mixture (from mixture 6 to mixture 9), as could be expected. Figure 6 shows the empirical WGPu alarm rate, i.e., the fraction of the measurements containing WGPu for which the estimated probability of WGPu presence is larger than 50%, as a function of the total photon counts (top) and WGPu counts (bottom) for the different WGPu -based mixtures, using the stilbene detector. With a target WGPu alarm rate of 80%, a few hundreds of counts from the WGPu source would set off the portal alarm, even in the presence of up to three other highly-radioactive masking sources. The highest number of approximately 3000 overall counts to trigger an alarm state is needed for mixture 5, which includes WPGu, 133 Ba, and 131 In. In similar irradiation conditions, in the presence of a mixed source, a detector similar to the one investigated would record approximately 130 counts during a 3-s vehicle scan time 8 . Assuming that the intrinsic efficiency scales with the volume of the detector and factoring an efficiency loss of 10% due to non-ideal light collection, a relatively small 2752 cm 3 single module used in portal monitors 19 would record approximately 3100 counts during a 3-s acquisition of a mixture of 133 Ba, 131 In, and WGPu. This acquisition time would be sufficient to set an alarm condition in the portal monitor. Regarding computational costs, the three competing methods (MMSE BTG , MMSE L1 and MAP L1 ) have been implemented using Matlab 2017b running on a MacBook Pro with 16 GB of RAM and a 2.9 GHz Intel Core i7 processor. Since the MMSE L1 is a simulation-based algorithm (see "Methods" section), its computational cost is significantly higher than the two other methods and it requires 66 s to analyze one spectrum (using 5000 iterations and assuming at most 11 sources in the mixture), on average. This prevents its use within portal monitors. Conversely, MAP L1 only takes 50-110 ms per spectrum and is the fastest method. Our new algorithm MMSE BTG is slower (approximately 1 s per spectrum) but still compatible with real-time monitoring. While slower than MAP L1 , MMSE BTG provides better estimates and allows automatic source detection and uncertainty quantification.

Discussion
RPMs must be able to detect weak SNM sources masked by a stronger NORM or nuisance radiation source. In this work, we overcame the limited energy resolution of organic scintillators by applying a new Bayesian algorithm to decompose and identify mixed gamma-ray sources. Bayesian algorithms proved to be useful tools to improve the source detection accuracy even with limited statistics (few counts) and poor signal-to-background ratios.
The proposed Bayesian MMSE BTG technique is designed to allow more accurate source identification and quantification in the presence of one or more masking nuclides, with cumulative count integrals as low as 500 counts. The automated identification obtained with the MMSE BTG method is more robust than using the MAP L1 and MMSE L1 algorithms, which require unpractical parameter tuning. The main benefit of the proposed method is a more sensitive model that captures the sparsity of the mixing coefficients. The application of the MMSE BTG reduces, for instance, the average root-mean-square error between real and estimated nuclide fractions to . 0 0177, compared to . 0 0334 for MAP L1 , and . 0 0584 for MMSE L1 for the sixth mixture, containing 99m Tc and WGPu, with only 1000 detection events. Our study also confirmed the importance of detector energy resolution. The stilbene crystal exhibits a better energy resolution than EJ-309 and, as a result, the stilbene data yielded a slightly better quantification accuracy, compared to EJ-309. Therefore, a slight improvement in the nuclide identification accuracy can be achieved by improving the energy resolution of the detector. Energy resolution improvement can be achieved either by using different materials, as we have shown in this study, and also by optimizing the detector's light collection geometry 20 . A relevant feature of organic scintillators is their sensitivity to both neutrons and gamma rays. Neutron and gamma-ray interactions in the organic scintillators are distinguishable through pulse  www.nature.com/scientificreports www.nature.com/scientificreports/ shape discrimination. The neutron signature was not used in this work but could be further exploited to aid the classification of fissile and other neutron emitting materials.
In this paper, we have applied new Bayesian algorithms for the identification of source mixtures that are not shielded. While this scenario applies to pedestrian portal monitors, it would be interesting to study the algorithm performance when sources are transported with other goods, or deliberately shielded. Effectively shielding SNMs and intense gamma-ray emitting radionuclides, such as 137 Cs and 60 Co, would require a combination of lowand high-atomic-number elements. The current algorithm could be enhanced by coupling it to spectra reconstruction methods that we have recently developed 21 , to account for the spectral effect of shielding materials, given their known gamma-ray and neutron attenuation coefficients, as proposed by Lawrence and colleagues 22 . It should also be noted that containers carrying covert or overt amounts of metal are likely to prompt secondary inspections. For example, cargo containers carrying a large number of metal items typically undergo radiation inspection because orphan sources are often improperly disposed of as scrap metal and can be cast into metal parts 23 . Conversely, electro-magnetic inspection is performed on cargoes that are declared metal-free, and would promptly identify covert metal items.

Methods
Over the past years, our group has developed several radionuclide identification algorithms for EJ-309-based portal monitors 6,8,12 . This work proposes a novel computational Bayesian method for source identification that we have applied to both liquid EJ-309 and solid-state trans-stilbene scintillators. In this section, we first detail how our measured data have been collected and then the principle of the new computational method. experimental methods. We have used two detectors: an EJ-309 organic liquid scintillator (7.6-cm diameter by 7.6-cm height) by Eljen Technology, and a cylindrical trans-stilbene crystal (5.08-cm diameter by 5.08-cm height) produced using the solution-growth technique by Inrad Optics. The detection system used can be easily scaled up to be a pedestrian portal by using an array of detector cells. Despite the similar composition, EJ-309 and stilbene exhibit different properties (see Table 2). Noticeably, EJ-309 has a higher scintillation efficiency and higher density, compared to stilbene, which determines its higher intrinsic detection efficiency 24 . However, the stilbene crystal shows a favorable energy resolution, defined as the full width at half maximum (FWHM) of a spectrum peak in response to the energy deposited in the detector by monoenergetic charged recoils, divided by its centroid. This improved energy resolution can enhance isotope identification accuracy using stilbene over EJ-309. Note that the energy resolution of a scintillation detector is affected by both the scintillating material and the light collection and conversion process. The energy resolution at 478 keVee of stilbene and EJ-309 detectors of the same size as those used in this work is 9.64 ± 0.06 25 and 19.33 ± 0.18 26 , respectively.
For completeness, Fig. 7 depicts the light output spectra of some of the mixtures analyzed, when approximately 1000 counts were acquired. Despite the spectra consisting of different nuclides, their overall distribution as a function of light output is similar. This effect is due to the scatter-based detection of organic scintillators and the low counting statistics.
We measured a variety of sources, including 241 Am, 133 Ba, 57 Co and 137 Cs sources with activities of approximately 500 kBq. The WGPu source (180 MBq) was measured at the Zero-Power Research Reactor of the Idaho National Laboratory 27 . In addition, 260 kBq liquid solution samples of the medical isotopes, i.e., 99m Tc, 111 In, 67 Ga, 123 I, 131 I, and 201 Tl were measured at the University of Michigan C.S. Mott Children's Hospital. The on-the-fly radionuclide identification algorithms used in this work rely on a library of nuclides that is assumed to include the species potentially present in the mixtures. The detection of unknown sources is out of the scope of this work and is left for future work. The isotope library used in this work consists of a collection of light output spectra acquired over one hour to reduce shot-noise effects. As the two detectors exhibit slightly different light responses, calibration was necessary to detect the same portion of the energy spectrum with both detectors. The detectors were gain-matched using a 3.3-MBq 137 Cs source, by aligning the 137 Cs Compton edge to 1.8 V in the pulse-height detector response. Lower and upper detection thresholds of 40 keV-electron-equivalent (keVee) and 480 keVee, respectively, were applied to both stilbene and EJ-309 detectors light output spectra. The electron-equivalent light output of a pulse in a scintillator, measured in electron-equivalent electron Volts, or eVee, refers to the energy required for an electron to produce a pulse with equivalent light output.  www.nature.com/scientificreports www.nature.com/scientificreports/ computational Method. Bayesian estimation: competing methods. Bayesian methods rely on exploiting the posterior distribution of variables of interest, by combining the observed data with additional prior information available about those variables. Here, we are interested in finding the coefficients associated with a set of nuclides. Numerous strategies have been proposed to solve this problem and, before introducing the proposed method, we first discuss the two methods used in 12 , namely, the MAP L1 and the MMSE L1 methods, to motivate the new MMSE BTG method.
Consider an observed spectral response = … y y y [ , , ] and gathered in the : , 1 ,: ,: . Each A m,: is a row vector gathering the spectral responses of the N known sources in the mth energy bin. Note that the spectral signatures are normalised such that they integrate to one and that this normalization has been performed using spectra measured with long integration times to reduce as much as possible shot-noise effects during the normalization. The amount/coefficient associated with the nth source is denoted by x n and the N coefficients are gathered in the vector . A classical approach to source separation is to assume as a first approximation, a linear mixing model which can be expressed in matrix/ vector form as ≈ y Ax. This model assumes that all the radiation sources present in the scene that are not included in the matrix A can be neglected. To avoid environment-dependent results, the background is neglected here. Our aim here is to study the nuclide identification and quantification in scenarios where the integration time is short and thus when the number of gamma detection events is low. In such cases, the observation noise corrupting each measurement can be accurately modeled by Poisson noise, leading to Poissonian form of the likelihood.
m m y m m ,: ,: m Since A is known, it is omitted in all the conditional distributions hereafter. Note that Eq. (2) implies that the sources present a fixed activity (or are static) during the integration time. In more complex scenarios, more complex models such as compound Poisson models might be used. Conditioned on the value of x, the entries of y are independently distributed, i.e., f fy fy Bayesian methods for spectral unmixing rely on additional prior information available about x to enhance its recovery from y. Such methods formulate a priori information through a prior distribution f x ( ) and the estimation of x can then be achieved using the posterior distribution The maximum a posteriori (MAP) estimate can be obtained by solving the following optimization problem x while the minimum mean squared error (MMSE) estimate, or posterior mean, can be obtained by computing the expectation E x [ ] f x y ( ) . Using a product of independent exponential prior distributions for x, leads to a model that is based on an  1 -norm penalty. This is the model used in our preliminary work 12 . In that work, we compared two approaches, namely, MAP estimation and MMSE estimation, leading to two algorithms, MAP L1 and MMSE L1 , respectively. It is important to mention that this choice of sparsity model is primarily motivated by the fact that the problem in (3) is convex and can be solved efficiently. While the MMSE L1 algorithm is based on Markov chain Monte Carlo (MCMC) methods and allows the estimation of a posteriori confidence intervals (which are not directly available with the MAP L1 method), we showed 12 that the proportions estimated were generally worse than when using MAP L1 . This is primarily due to the fact that although exponential prior distributions promote sparse MAP estimates; this family of distributions is not sparsity promoting (it only tends to concentrate the mass of the distribution around the origin). Hence, the resulting probabilistic estimates, such as means or covariances are questionable 28 . This observation is also confirmed with the results in Fig. 2. Our previous study 12 also showed that www.nature.com/scientificreports www.nature.com/scientificreports/ by constraining ≤ K N the maximum number of sources present in each mixture, it is possible to further improve the unmixing performance using MAP L1 . This improvement however comes at a high computational cost as it requires comparing all the possible partitions of K sources, out of N sources in the original spectral library. This becomes rapidly intractable as N increases. It also requires a level of supervision (to set K properly) which is incompatible with practical, real-time applications.
Alternative prior model for sparse mixtures. In this work, we first propose to use an alternative, more efficient, sparsity-promoting prior model for x. Precisely, we consider the following Bernoulli-truncated Gaussian (BTG) model , i.e., at performing jointly the source identification (through w) and quantification (through x). Note that {π n } n and σ { } n 2 are assumed to be known here and can be used-defined. For the prior probabilities of presence, we set π = ∀ N n 1/ , n as we expect a limit number of sources to be simultaneously present in the mixture, while we do not wish to promote any specific source. While arbitrary large values could in principle be used for the variances σ { } n 2 , reflecting the lack of information about the activity of the sources to be detected, this strategy can lead to poor detection 29 . If the variances cannot be set from prior knowledge, an alternative approach, adopted here consists of adjusting it using the current observation, in an empirical Bayes fashion. Since the matrix A is normalised, the variances σ { } n . While less well known than other Variational Bayes (VB) techniques, the EP has several recognized advantages 34 . It is particularly well suited to fast distributed Bayesian inference on partitioned data, giving it a high potential for real-time implementation.
The EP framework used for regression with Gaussian noise 35   where all the approximate factors belong to the same family of distributions. Here, in a similar fashion to the work by Hernandez-Lobato et al. 37 , the approximate factors dependent on x are Gaussian and those associated with each w n are discrete probabilities (see Fig. 8). This choice allows a more computationally attractive EP algorithm