Recovering radionuclide contributions from y-ray spectra is a central task in nuclear signal processing, which goal is to estimate both the underlying source spectra and their proportions in a measured signal. This source separation problem relies on prior spectral knowledge to guide the estimation, but it remains challenging due to noise and spectral variabilities due to not well-known measurement conditions, caused by y-photon interactions in the source surroundings or differing source geometries. The problem is semi-blind in nature: the radionuclide sources are known, but their exact spectral responses are unknown. Existing unmixing algorithms either rely on iterative solvers which are slow, or use "black-box" neural networks overlooking the underlying physical structure of the problem. In this work, we propose GLUPSS, a Generative Learned Unrolling algorithm for Poisson Source Separation. Our approach leverages the statistical nature of the data by incorporating a Poisson log-likelihood loss and models the spectral variability using a 1D manifold learned through a generative Interpolating AutoEncoder (IAE). Furthermore, building on algorithm unrolling, we propose a neural network which mimics a proximal optimization scheme but drastically reduces the number of iterations, making GLUPSS usable for real-life, time-sensitive applications. Experimental results on realistic synthetic data show that GLUPSS achieves an estimation accuracy within 1% (in terms of Absolute Relative Error) of the state-of-the-art SEMSUN iterative methods while offering a 60 & times; speedup compared to this method.1

During the last decade, a large number of different numerical methods have been proposed to tackle the automatic identification and quantification in y-ray spectrometry. However, the lack of common benchmarks, including datasets, code and comparison metrics, makes their evaluation and comparison hard. In that context, we propose an open-source benchmark that comprises simulated datasets of various y-spectrometry settings, codes of different analysis approaches and evaluation metrics. This allows us to compare the state-of-the-art end-to-end machine learning with a statistical unmixing approach using the full spectrum. Three scenarios have been investigated: (1) spectral signatures are assumed to be known; (2) spectral signatures are deformed due to physical phenomena such as Compton scattering and attenuation; and (3) spectral signatures are shifted (e.g., due to temperature variation). A large dataset of 2.105 simulated spectra containing nine radionuclides with an experimental natural background is used for each scenario with multiple radionuclides present in the spectrum. Regarding identification performance, the statistical approach consistently outperforms the machine learning approaches across all three scenarios for all comparison metrics. However, the performance of the statistical approach can be significantly impacted when spectral signatures are not modeled correctly. Consequently, the full-spectrum statistical approach is most effective with known or well-modeled spectral signatures, while end-to-end machine learning is a good alternative when measurement conditions are uncertain for radionuclide identification. Concerning the quantification task, the statistical approach provides accurate estimates of radionuclide counting, while the machine learning methods deliver less satisfactory results.

Identifying and quantifying γ-emitting radionuclides, considering spectral deformation from γ-interactions in radioactive source surroundings, present a significant challenge in γ-ray spectrometry. In that context, a hybrid machine learning method has been previously proposed to jointly estimate the counting and spectral signatures of γ-emitters under conditions of spectral variability. This paper addresses the uncertainty quantification of the estimators (i.e., the counting and the variable λ which characterizes the spectral signatures) obtained by this spectral unmixing algorithm. The focus is on the coverage interval, as defined by the GUM, which corresponds closely to a credible interval in the Bayesian framework. Given the inverse problem and the constraints associated with spectral deformation, two Bayesian methods - Laplace approximation and Markov Chain Monte Carlo - have been developed for uncertainty quantification to ensure robust decision-making. The Laplace approximation technique approximates the posterior distribution by a Gaussian distribution, while the Markov Chain Monte Carlo technique samples the posterior distribution. This study evaluates these two methods in terms of precision of coverage interval based on repeated Monte Carlo samples using the long-run success rate. Numerical experiments show that both methods yield similar results close to the expected success rate of 95.4% when constraints related to spectral signatures deformation and counting are inactive. However, when constraints are active or the background counting significantly dominates other radionuclides, the Laplace approximation method deviates from the expected long-run success rate due to the non-Gaussian posterior distribution. In such cases, the Markov Chain Monte Carlo method still provides robust results.

Gamma-ray spectrometry is a widely used technique for identifying and quantifying γ-emitting radionuclides in many nuclear applications. Currently, there is a growing trend to address the problem of automatic identification of radionuclides by implementing machine learning (ML) approaches such as multilayer perceptrons (MLP) or convolutional neural networks (CNN). Alongside these ML methods, the statistical method based on full-spectrum analysis with Poisson likelihood yields reliable results. However, due to the lack of a common benchmark, a comparison of these methods has not yet been conducted. In this work, we introduce a benchmark to evaluate and compare these methods under three scenarios: (1) known spectral signatures, (2) spectra deformed by physical phenomena and (3) gain shift. A large dataset of 200000 simulated spectra was generated for each scenario, spanning a broad range of radionuclide combinations and mixing ratios. This work utilizes a dictionary of nine radionuclide spectral signatures generated with the Monte Carlo code Geant4 for a 3"×3" NaI(Tl) detector, combined with an experimental natural background. For the ML method, we trained a dedicated CNN model for each scenario, carefully optimized its hyperparameters, and adjusted its classification threshold. The results show that the statistical method consistently outperforms the ML approach across all scenarios, particularly under low-statistics conditions. Furthermore, the statistical method maintains a false positive rate close to the predefined level.

Automatic identification and quantification of y-emitting radionuclides, considering the spectral deformation due to y-interactions in the radioactive source environment, is a demanding challenge in the field of nuclear physics. In this context, this paper presents a hybrid unmixing approach combining a pre-trained machine learning model (autoencoder) to capture spectral deformations and a model selection technique based on statistical testing to identify the radionuclides present in a radioactive source and quantify their mixing weights. The identification process of radionuclides is based on a sequential selection algorithm using a likelihood ratio test depending on the expected false positives. Basically, this method aims to minimize the number of radionuclides in an initial radionuclide library containing characteristic y-spectra of each y-emitter to be tested. The robustness of decision-making with this approach and the quantification performance are investigated with Monte Carlo simulations involving up to 12 radionuclides to be tested, according to different mixture scenarios with increasing complexity and various statistics. The false positive rates obtained with the hybrid unmixing approach are close to the expected values. In general, the quantification results are similar to the case when the radionuclides present in the source and spectral signatures are known. This highlights the effectiveness of this novel hybrid unmixing approach for the automatic identification and quantification of gamma-ray emitting radionuclides with spectral variability.

The Laser Interferometer Space Antenna (LISA) mission is being developed by ESA with NASA participation. As it has recently passed the Mission Adoption milestone, models of the instruments and noise performance are becoming more detailed, and likewise prototype data analyses must as well. Assumptions such as Gaussianity, stationarity, and data continuity are unrealistic, and must be replaced with physically motivated data simulations, and data analysis methods adapted to accommodate such likely imperfections. To this end, the LISA Data Challenges have produced datasets featuring time-varying and unequal constellation armlength, and measurement artifacts including data interruptions and instrumental transients. In this work, we assess the impact of these data artifacts on the inference of Galactic Binary and Massive Black Hole properties. Our analysis shows that the treatment of noise transients and gaps is necessary for effective parameter estimation, as they substantially corrupt the analysis if unmitigated. We find that straightforward mitigation techniques can significantly if imperfectly suppress artifacts. For the Galactic Binaries, mitigation of glitches was essentially total, while mitigations of the data gaps increased parameter uncertainty by approximately 10%. For the Massive Black Hole binaries the particularly pernicious glitches resulted in a 30% uncertainty increase after mitigations, while the data gaps can increase parameter uncertainty by up to several times. Critically, this underlines the importance of early detection of transient gravitational waves to ensure they are protected from planned data interruptions.

Context. The space-based gravitational wave observatory LISA will provide a wealth of information to analyze massive black hole binaries with high chirp masses, beyond 105 solar masses. The large number of expected MBHBs (one event a day on average) increases the risk of overlapping between events. As well, the data will be contaminated with non-stationary artifacts, such as glitches and data gaps, which are expected to strongly impact the MBHB analysis, which mandates the development of dedicated detection and retrieval methods on long time intervals. Aims. Building upon a methodological approach we introduced for galactic binaries, in this article we investigate an original non-parametric recovery of MBHB signals from measurements with instrumental noise typical of LISA in order to tackle detection and signal reconstruction tasks on long time intervals. Methods. We investigated different approaches based on sparse signal modeling and machine learning. In this framework, we focused on recovering MBHB waveforms on long time intervals, which is a building block to further tackling more general signal recovery problems, from gap mitigation to unmixing overlapped signals. To that end, we introduced a hybrid method called SCARF (sparse chirp adaptive representation in Fourier), which combines a deep learning modeling of the merger of the MBHB with a specific adaptive time-frequency representation of the inspiral. Results. Numerical experiments have been carried out on simulations of single MBHB events that account for the LISA response and with realistic realizations of noise. We checked the performances of the proposed hybrid method for the fast detection and recovery of the MBHB.

Direct detection of the Cosmic Dawn and Epoch of Reionization via the redshifted 21-cm line of neutral Hydrogen will have unprecedented implications for studying structure formation in the early Universe. This exciting goal is challenged by the difficulty of extracting the faint 21-cm signal buried beneath bright astrophysical foregrounds and contaminated by numerous systematics. Here, we focus on improving the Gaussian Process Regression (GPR) signal separation method originally developed for LOFAR observations. We address a key limitation of the current approach by incorporating covariance prior models learnt from 21-cm signal simulations using Variational Autoencoder (VAE) and Interpolatory Autoencoder (IAE). Extensive tests are conducted to evaluate GPR, VAE-GPR, and IAE-GPR in different scenarios. Our findings reveal that the new method outperforms standard GPR in component separation tasks. Moreover, the improved method demonstrates robustness when applied to signals not represented in the training set. It also presents a certain degree of resilience to data systematics, highlighting its ability to effectively mitigate their impact on the signal recovery process. However, our findings also underscore the importance of accurately characterizing and understanding these systematics to achieve successful detection. Our generative approaches provide good results even with limited training data, offering a valuable advantage when a large training set is not feasible. Comparing the two algorithms, IAE-GPR shows slightly higher fidelity in recovering power spectra compared to VAE-GPR. These advancements highlight the strength of generative approaches and optimise the analysis techniques for future 21-cm signal detection at high redshifts.

Automatic identification and quantification of γ-emitting radionuclides, taking into account spectral deformations due to γ-interactions in radioactive source surroundings, is a challenging task in the nuclear field. In that context, this paper presents a Machine Learning approach based on autoencoder that can learn a model for the spectral signatures of γ-emitters with variability. Training and test datasets were obtained by means of simulated γ-spectra computed with the Geant4 simulation code according to increasing material thicknesses (steel, lead). A novel hybrid unmixing algorithm combining a pretrained autoencoder is studied for joint estimation of spectral signatures and counting in the case of mixtures of four radionuclides (57Co, 60Co, 133Ba, 137Cs). The investigations were carried out to account for spectral deformations due to attenuation, Compton scattering and fluorescence at high and low statistics. This study demonstrates the validity of this novel hybrid approach combining Machine Learning and Maximum Likelihood for the automatic full-spectrum analysis of γ-spectra.

The advent of next-generation radio interferometers like the Square Kilometer Array promises to revolutionise our radio astronomy observational capabilities. The unprecedented volume of data these devices generate requires fast and accurate image reconstruction algorithms to solve the ill-posed radio interferometric imaging problem. Most state-of-the-art reconstruction methods lack trustworthy and scalable uncertainty quantification, which is critical for the rigorous scientific interpretation of radio observations. We propose an unsupervised technique based on a conformalized version of a radio-augmented equivariant bootstrapping method, which allows us to quantify uncertainties for fast reconstruction methods. Noticeably, we rely on reconstructions from ultra-fast unrolled algorithms. The proposed method brings more reliable uncertainty estimations to our problem than existing alternatives.

The automatic identification and quantification of gamma-emitting radionuclides, accounting for spectral deformation due to gamma interactions in the environment of radioactive sources, is a challenge for various nuclear applications. In this paper, this problem is addressed by developing a hybrid approach combining Machine Learning and classical statistical methods. A specific Machine Learning-based autoencoder that can capture spectral variability with limited data is proposed. A novel hybrid unmixing algorithm employing a pre-trained autoencoder is investigated for joint estimation of spectral signatures and counting in the case of mixtures of four radionuclides (Co-57, Co-60, Ba-133, Cs-137). This study was carried out to take account of spectral deformation due to attenuation and Compton scattering at low statistics. The results demonstrate the validity of this new hybrid approach based on Machine Learning and Maximum Likelihood for the automatic full-spectrum analysis of gamma-spectra.

A challenging problem in gamma-ray spectrum analysis is the rapid detection of artificial radionuclides at low activity levels. Until now, traditional methods focus on activity estimation based on single spectra, obtained by integrating over time the measured disintegration events. However, accounting for the well-constrained radionuclides decay should allow for a more accurate and sensitive activity estimation. For that purpose, we investigate a novel approach to estimate radionuclides' activity, which is (i) first based on multi-temporal data, obtained from several short measurements rather than a single one, and (ii) built upon a dedicated spectral unmixing, which allows processing multi-temporal data. The proposed algorithm allows accounting for both the full spectrum of each radionuclide (i.e. peaks and Compton continuum) and their activity decay in time. To that purpose, different approaches are investigated to model the temporal dependencies of the radionuclides' activities, and specifically to account for potentially out of equilibrium radionuclides' decay chains. Experimental results on both simulated spectra and real measurements are presented and compared to standard methods, it is shown that the proposed approach leads to more accurate estimations and faster detection of artificial radionuclides.

With the fastly increasing development of multichannel imagers, blind source separation (BSS) algorithms are ubiquitous in astrophysics to unmix multispectral images. In this context, analyzing data from the forthcoming very large, continental-size, radio interferometers using BSS algorithms raises two challenges. Firstly, the data are incomplete and deteriorated by instrumental effects, which requires incorporating a deconvolution step to retrieve exploitable images. Secondly, the data are affected by non-coplanar effects that notably arise from the very large antenna baselines and which must be accounted for in the separation scheme. For this purpose, we introduce a joint non-coplanar deconvolution and BSS algorithm, called wGMCA. The algorithm is tested and characterized in many challenging configurations, showing remarkable robustness to initialization and inversion. It is compared to classical methods that process the deconvolution and separation separately; these tests demonstrate the advantage of performing the deconvolution and separation in a single pass.

Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires efficient regularization schemes to better distinguish between the sources and yield interpretable solutions. For that purpose, we investigate a semi-supervised source separation approach in which we combine a projected alternating least-square algorithm with a learning-based regularization scheme. In this article, we focus on constraining the mixing matrix to belong to a learned manifold by making use of generative models. Altogether, we show that this allows for an innovative BSS algorithm, with improved accuracy, which provides physically interpretable solutions. The proposed method, coined sGMCA, is tested on realistic hyperspectral astrophysical data in challenging scenarios involving strong noise, highly correlated spectra and unbalanced sources. The results highlight the significant benefit of the learned prior to reduce the leakages between the sources, which allows an overall better disentanglement.

Hyperspectral images (HI) are cubes of data with two spatial dimensions and a third spectral dimension. In this paper, we present SUSHI (Semi Blind Unmixing with Sparsity for Hyperspectral Images), an algorithm for unmixing HI with spectral variability that can be described by a physical model, which need not be analytical. To obtain a differentiable, parametric surrogate spectral model, we use a network called an Interpolatory Auto-Encoder (IAE), and plug it in a state-of-the-art optimizing architecture for solving regularized inverse model. We apply a constraint of spatial regularization on the latent parameters, to account for correlations between pixels instead of treating them individually. We test SUSHI on a toy-model inspired by supernova remnants as seen by the X-ray telescope Chandra. Our results are a net improvement on those obtained with the classic method which is usually applied in the astrophysics community.

We introduced in a previous paper a time-dependent full-spectrum analysis algorithm speeding up the estimation of the activity of the radionuclides present in a sample. In this paper, we present a new version of the algorithm allowing online estimation. It uses only on a buffer of few segments while keeping the time information by using a time dependent regularization, thus reducing the size of the data matrices and the length of the processing of each iteration. The algorithm is optimized and tested on both simulated and measured spectra of aerosol samples.

Signal unmixing is a class of complex, ill-posed inverse problems, which includes blind source separation or underdetermined signal separation to cite only two. Retrieving signals from their mixtures generally relies on adapted representations allowing to disentangle them. When dealing with real-world scientific data, the main challenge is to further build meaningful signal representations, which generally means capturing the underlying low-dimensional manifold structure of the signals to be recovered. Since the latter is generally unknown, this calls for a learning-based approach, which is a challenging task, especially when available training samples are scarce. The objective of the paper is to investigate a new learning model to build low-dimensional signal representations from few training samples. Based on an encoder-decoder architecture, the proposed approach aims to learn a non-linear interpolating scheme from examples. Extensive numerical experiments have been carried out to evaluate the performances of the proposed approach. We further illustrate how the learned representations can be conveniently deployed to tackle challenging semi-blind unmixing problems in the field of γ-ray spectroscopy.

The forthcoming space-based gravitational wave observatory LISA will open a new window for the measurement of galactic binaries, which will deliver unprecedented information about these systems. However, the detection of galactic binary gravitational wave signals is challenged by the presence of gaps in the data. Whether being planned or not, gapped data reduce our ability to detect faint signals and increase the risk of misdetection. Inspired by advances in signal processing, we introduce a non-parametric inpainting algorithm based on the sparse representation of the galactic binary signal in the Fourier domain. In contrast to traditional inpainting approaches, noise statistics are known theoretically on ungapped measurements only. This calls for the joint recovery of both the ungapped noise and the galactic binary signal. We thoroughly show that sparse inpainting yields an accurate estimation of the gravitational imprint of the galactic binaries. Additionally, we highlight that the proposed algorithm produces a statistically consistent ungapped noise estimate. We further evaluate the performances of the proposed inpainting methods to recover the gravitational wave signal on a simple example involving verification galactic binaries recently proposed in LISA data challenges.

Poisson-statistics based spectral unmixing has been shown to be an efficient analysis tool for the radionuclides activity estimation from gamma-ray spectrometry measurements. However, the calculation of the corresponding characteristic limits has not been investigated so far. In this paper, we present the quantification of the decision threshold and the limits of the coverage interval for the metrological use of such spectral unmixing algorithms. The proposed approach is evaluated and validated with simulated spectra of HPGe and NaI measurements by comparing the results to characteristic limits calculated from Monte-Carlo simulations. We focus particularly on the validation of the method for the metrological analysis of environmental measurements, for which the low-level activity quantification requires an accurate characteristic limits determination. Along with the instrument calibration, we establish a metrological analysis tool by using the spectral unmixing algorithm for environmental aerosol filters measured by gamma-ray spectrometry.

In the context of radioactivity measurements, the quantitative analysis of a gamma-ray spectrum depends on the analysis algorithm. To that end, we recently introduced a Poisson statistics-based spectral unmixing approach. However, it also relies on a proper instrument recalibration as well as on an uncertainty estimation, for which no solution has been proposed so far. The goal of this article is twofold: i) we first present a novel method to correct for the instrument calibration of an HPGe detection system, which is tailored to spectral unmixing algorithms, and ii) we apply this new approach to the quantitative analysis of real data as well as on the evaluation of the uncertainty. Along with the characteristic limits determination investigated, this paper introduces the first full metrological analysis sequence of aerosol filter measurements based on spectral unmixing, which allows to quantify both the radionuclides' activities and their associated uncertainties.