X-ray interaction with matter is an energy-dependent process that is contingent on the atomic structure of the constituent material elements. The most advanced models to capture this relationship currently rely on Monte Carlo (MC) simulations. Whilst these very accurate models, in many problems in spectral X-ray imaging, such as data compression, noise removal, spectral estimation, and the quantitative measurement of material compositions, these models are of limited use, as these applications typically require the efficient inversion of the model, that is, they require the estimation of the best model parameters for a given spectral measurement. Current models that can be easily inverted however typically only work when modelling spectra in regions away from their K-edges, so they have limited utility when modelling a wider range of materials. In this paper, we thus propose a novel, non-linear model that combines a deep neural network autoencoder with an optimal linear model based on the Singular Value Decomposition (SVD). We compare our new method to other alternative linear and non-linear approaches, a sparse model and an alternative deep learning model. We demonstrate the advantages of our method over traditional models, especially when modelling X-ray absorption spectra that contain K-edges in the energy range of interest.

翻译：X射线与物质的相互作用是一个依赖于能量的过程，其具体机制取决于构成材料元素的原子结构。目前最先进的建模方法依赖于蒙特卡罗（MC）模拟。尽管这些模型非常精确，但在光谱X射线成像的许多问题中——如数据压缩、噪声去除、光谱估计以及材料组分的定量测量——这些模型的应用价值有限，因为这些应用通常需要模型的高效可逆性，即根据给定的光谱测量结果估计最佳模型参数。然而，当前易于逆化的模型通常仅适用于K边以外的光谱区域建模，因此在更广泛材料的建模中实用性受限。为此，本文提出一种结合深度神经网络自编码器与基于奇异值分解（SVD）的最优线性模型的新型非线性模型。我们将新方法与替代线性/非线性方法、稀疏模型及另一种深度学习模型进行对比，并证明该方法相比传统模型的优势，尤其在建模包含感兴趣能量范围内K边的X射线吸收光谱时表现显著。