This paper presents a metrological approach of spectral unmixing for automatic identification and quantitative analysis of γ-emitting radionuclides in natural background radiation at low statistics. Based on full-spectrum analysis, the proposed method relies on the maximum likelihood estimation based on Poisson statistics that accounts for the spectral signatures of the γ-emitters to be identified and natural background. In order to obtain robust decision-making at low statistics, a sparsity constraint is implemented along with counting estimation given by spectral unmixing. In contrast with the standard approach, this technique relies on a single decision threshold applied for a likelihood ratio test. Standard deviations on estimated counting are determined using the Fisher information matrix. The robustness of decision-making and counting estimation was investigated by means of Monte Carlo calculations based on experimental spectral signatures of two types of scintillation detectors [NaI(Tl), plastic]. This study demonstrates that sparse spectral unmixing is a reliable method for γ-spectra analysis based on low-level measurements. The sparsity constraint acts as an efficient technique for decision-making in the case of complex mixtures of γ-emitters with significant contribution of natural background. This method also yields unbiased counting estimation related to the identified radionuclides. Reliable assessment of standard deviations are obtained and the Gaussian approximation of the coverage intervals is validated. The proposed method can be applied either by non-expert users for automatic analysis of γ-spectra or to help experts in decision-making in the case of complex mixtures of γ-emitters at low statistics.

本文提出了一种光谱分解的计量学方法，该方法可自动识别和定量分析自然背景辐射中γ发射的放射性核素，而其统计量较低。基于全光谱分析，提出的方法依赖于基于泊松统计的最大似然估计，该估计考虑了要识别的γ发射体的光谱特征和自然本底。为了在低统计量下获得可靠的决策，将稀疏约束与频谱分解混合给出的计数估计一起实施。与标准方法相反，此技术依赖于应用于似然比测试的单个决策阈值。估计计数的标准偏差使用Fisher信息矩阵确定。基于两种闪烁探测器[NaI（Tl），塑料]的实验光谱特征，通过蒙特卡洛计算研究了决策和计数估计的鲁棒性。这项研究表明，稀疏光谱分解是基于低水平测量进行γ光谱分析的可靠方法。稀疏约束是在自然背景有重要贡献的复杂的γ发射体混合物的情况下，作为一种有效的决策方法。该方法还产生与所识别的放射性核素有关的无偏计数估计。获得了标准偏差的可靠评估，并验证了覆盖区间的高斯近似。