Laser induced breakdown spectroscopy for quantitative analysis based on low-rank matrix approximations,Journal of Analytical Atomic Spectrometry

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Laser induced breakdown spectroscopy for quantitative analysis based on low-rank matrix approximations
Journal of Analytical Atomic Spectrometry ( IF 3.1 ) Pub Date : 2017-07-12 00:00:00 , DOI: 10.1039/c7ja00178a
Cancan Yi _{1,

2,

3,

4,

5} , Yong Lv _{2,

3,

4,

5,

6} , Han Xiao _{2,

3,

4,

5,

6} , Shan Tu _{4,

7,

8,

9}

Affiliation

In quantitative laser-induced breakdown spectroscopy (LIBS) analysis, spectral signals are usually represented by the linear combination of characteristic peaks with useful spectral information and unwanted noise components. All of the existing regression analysis methods are related to a spectral data matrix, which is composed of certified samples with different spectral intensity. Therefore, spectral data matrix processing is critical for quantitative LIBS analysis. A prevalent assumption when constructing a matrix approximation is that the partially observed matrix is of low-rank. Moreover, the low-rank structure always reflects the useful information and is regarded as a powerful data preprocessing method. In this paper, a novel and quantitative LIBS analysis method based on a sparse low-rank matrix approximation via convex optimization is proposed. Based on the sparsity of the spectral signals, we present a convex objective function consisting of a data-fidelity term and two parameterized penalty terms. To improve the accuracy of the quantitative analysis, a new non-convex and non-separable penalty based on the Moreau envelope is proposed. Then, the alternating direction method of multipliers (ADMM) algorithm was utilized to solve the optimization problem. The proposed method was applied to the quantitative analysis of 23 high alloy steel samples. Both of the performances of the Partial Least Squares (PLS) and Support Vector Machine (SVM) regression models are improved by using the low-rank matrix approximation scheme, which proves the effectiveness of the proposed method.

中文翻译：

激光诱导击穿光谱法用于基于低秩矩阵近似的定量分析

在定量激光诱导击穿光谱（LIBS）分析中，光谱信号通常由特征峰与有用光谱信息和有害噪声成分的线性组合表示。所有现有的回归分析方法都与光谱数据矩阵有关，该光谱数据矩阵由具有不同光谱强度的认证样本组成。因此，光谱数据矩阵处理对于定量LIBS分析至关重要。构建矩阵近似时，普遍的假设是部分观察到的矩阵是低秩的。而且，低等级结构总是反映有用的信息，并被认为是一种强大的数据预处理方法。在本文中，一种新颖的和定量的分析LIBS方法基于稀疏低秩矩阵近似经由提出了凸优化。基于频谱信号的稀疏性，我们提出了一个凸目标函数，该目标函数由数据保真度项和两个参数化的惩罚项组成。为了提高定量分析的准确性，提出了一种基于莫罗包络的非凸且不可分离的罚分方法。然后，采用交替方向乘数法（ADMM）算法解决了优化问题。该方法用于23种高合金钢样品的定量分析。通过使用低秩矩阵逼近方案，改进了偏最小二乘（PLS）和支持向量机（SVM）回归模型的性能，证明了该方法的有效性。

更新日期：2017-11-02

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