In typical spectrometric measurement systems, a high-resolution spectrum is obtained directly via sequential observations with a narrow slit-like measurement window at the expense of sensitivity. In this paper, we propose a novel spectrometric method applicable to these typical spectrometric systems: a multiplexed low-resolution measurement with a wide measurement window, band measurement (BM), is combined with sparse-modeling-based post-processing to obtain the original high-resolution spectrum. BM is expected to improve the measurement signal-to-noise ratio because of the increase in the sample quantities reaching the detector by widening the measurement window. BM has the significant practical advantage that it can be easily implemented in spectrometric measurement systems without device alterations. To evaluate the effectiveness of our proposal both theoretically and experimentally, we formulate the sparse-modeling-based post-processing in the proposal in terms of the least absolute shrinkage and selection operator (lasso) and perform a theoretical analysis and simulation studies concerning the resulting spectrometric method named BM-lasso. In the theoretical analysis, we derive density evolution equations for belief propagation on the BM-lasso model and obtain the expected errors of estimators of BM-lasso. The numerical evaluations of the theoretical analysis result revealed that BM-lasso achieved lower mean square error than the conventional measurement method under the same parameter conditions. Furthermore, simulation studies with both artificial and actual mass spectra show that BM-lasso significantly improves the accuracy, sensitivity, and specificity compared with the conventional measurement method, demonstrating the practicality of the proposed method.

中文翻译：

---

基于谱带测量的光谱仪稀疏建模


在典型的光谱测量系统中，通过使用窄缝状测量窗口的连续观察直接获得高分辨率光谱，但牺牲了灵敏度。在本文中，我们提出了一种适用于这些典型光谱测量系统的新型光谱测量方法：具有宽测量窗口的多路低分辨率测量，波段测量（BM），与基于稀疏建模的后处理相结合，以获得原始光谱高分辨率光谱。由于通过加宽测量窗口增加了到达检测器的样本量，BM 有望提高测量信噪比。 BM 具有显着的实际优势，可以在光谱测量系统中轻松实现，无需更改设备。为了从理论上和实验上评估我们建议的有效性，我们根据最小绝对收缩和选择算子（套索）在建议中制定了基于稀疏建模的后处理，并对所得结果进行了理论分析和模拟研究。称为 BM-lasso 的光谱测量方法。在理论分析中，我们推导了BM-lasso模型上信念传播的密度演化方程，并得到了BM-lasso估计量的期望误差。理论分析结果的数值评估表明，在相同参数条件下，BM-lasso比传统测量方法取得了更低的均方误差。此外，人工和实际质谱的模拟研究表明，与传统测量方法相比，BM-lasso 显着提高了准确性、灵敏度和特异性，证明了该方法的实用性。