大气气体混合物差分光学吸收光谱的半盲源分离方法
A Semi-Blind Source Separation Method for Differential Optical Absorption Spectroscopy of Atmospheric Gas Mixtures
AI总结：
提出一种三步半盲源分离方法，通过多分辨率分析、凸优化和盲独立成分分析，从差分光学吸收光谱中识别未知痕量气体。
摘要：
差分光学吸收光谱（DOAS）是检测和量化大气化学中痕量气体的有力工具\cite{Platt_Stutz08}。DOAS光谱由复杂的多峰多尺度结构的线性组合组成。目前使用的大多数DOAS分析程序基于最小二乘技术，例如，1970年代开发的方法使用多项式拟合去除缓慢变化的背景，并使用已知参考光谱来检索参考气体的身份和浓度。一个开放的问题是在复杂大气混合物的拟合残差中识别未知气体。在这项工作中，我们开发了一种新颖的三步半盲源分离方法。第一步使用多分辨率分析去除DOAS光谱数据矩阵$X$中的慢变和快变成分。第二步将第一步预处理后的数据$\hat{X}$分解为参考光谱的线性组合加上余项，即$\hat{X} = A\,S + R$，其中矩阵$A$的列是已知参考光谱，矩阵$S$包含与浓度成正比的未知非负系数。第二步通过凸最小化问题$S = \mathrm{arg} \min \mathrm{norm}\,(\hat{X} - A\,S)$实现，其中范数是混合$\ell_1/\ell_2$范数（Huber估计器），有助于保持$S$的非负性。第三步对余项矩阵$R$进行盲独立成分分析，以提取残余气体成分。我们首先通过从余项矩阵中令人满意地盲提取一个先验未知的痕量气体（臭氧）来说明所提出的方法在处理一组DOAS实验数据中的效果。数值结果还表明，该方法可以从残差中识别多种痕量气体。
英文摘要：
Differential optical absorption spectroscopy (DOAS) is a powerful tool for detecting and quantifying trace gases in atmospheric chemistry \cite{Platt_Stutz08}. DOAS spectra consist of a linear combination of complex multi-peak multi-scale structures. Most DOAS analysis routines in use today are based on least squares techniques, for example, the approach developed in the 1970s uses polynomial fits to remove a slowly varying background, and known reference spectra to retrieve the identity and concentrations of reference gases. An open problem is to identify unknown gases in the fitting residuals for complex atmospheric mixtures. In this work, we develop a novel three step semi-blind source separation method. The first step uses a multi-resolution analysis to remove the slow-varying and fast-varying components in the DOAS spectral data matrix $X$. The second step decomposes the preprocessed data $\hat{X}$ in the first step into a linear combination of the reference spectra plus a remainder, or $\hat{X} = A\,S + R$, where columns of matrix $A$ are known reference spectra, and the matrix $S$ contains the unknown non-negative coefficients that are proportional to concentration. The second step is realized by a convex minimization problem $S = \mathrm{arg} \min \mathrm{norm}\,(\hat{X} - A\,S)$, where the norm is a hybrid $\ell_1/\ell_2$ norm (Huber estimator) that helps to maintain the non-negativity of $S$. The third step performs a blind independent component analysis of the remainder matrix $R$ to extract remnant gas components. We first illustrate the proposed method in processing a set of DOAS experimental data by a satisfactory blind extraction of an a-priori unknown trace gas (ozone) from the remainder matrix. Numerical results also show that the method can identify multiple trace gases from the residuals.
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