Laser induced breakdown spectroscopy for quantitative analysis based on low-rank matrix approximations

Abstract

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.