Airborne gamma-ray surveys are useful for many applications, ranging from geology and mining to public health and nuclear security. In all these contexts, the ability to decompose a measured spectrum into a linear combination of background source terms can provide useful insights into the data and lead to improvements in the techniques that use spectral energy windows. Multiple methods for the linear decomposition of spectra exist but are subject to various drawbacks, such as allowing negative photon fluxes or requiring detailed Monte Carlo modeling. We propose using non-negative matrix factorization (NMF) as a data-driven approach to spectral decomposition. Using aerial surveys that include flights over water, we demonstrate that the mathematical approach of NMF finds physically relevant structure in the aerial gamma-ray background, namely, that measured spectra can be expressed as the sum of nearby terrestrial emission, distant terrestrial emission, and radon and cosmic emission. These NMF background components are compared with the background components obtained by noise-adjusted singular value decomposition (NASVD), which contain negative photon fluxes and, thus, do not represent the emission spectra in as straightforward a way. Finally, we comment on the potential areas of research that are enabled by NMF decompositions, such as new approaches to spectral anomaly detection and data fusion.

中文翻译：

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使用非负矩阵分解对空中伽马射线背景进行建模


机载伽马射线勘测可用于许多应用，从地质和采矿到公共卫生和核安全。在所有这些情况下，将测量的光谱分解为背景源项的线性组合的能力可以提供对数据的有用见解，并导致使用光谱能量窗的技术的改进。存在多种光谱线性分解方法，但存在各种缺点，例如允许负光子通量或需要详细的蒙特卡罗建模。我们建议使用非负矩阵分解（NMF）作为数据驱动的谱分解方法。通过使用包括水上飞行在内的航空勘测，我们证明了 NMF 的数学方法可以在航空伽马射线背景中找到物理相关的结构，即测量的光谱可以表示为附近地面发射、远处地面发射和氡气和宇宙发射。将这些 NMF 背景分量与通过噪声调整奇异值分解 (NASVD) 获得的背景分量进行比较，后者包含负光子通量，因此不能以直接的方式表示发射光谱。最后，我们评论了 NMF 分解所支持的潜在研究领域，例如光谱异常检测和数据融合的新方法。