MACHINE REGRESSION-MODEL; CONVEX-OPTIMIZATION; COEFFICIENTS; LIBS

In quantitative laser-induced breakdown spectroscopy 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 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 and Support Vector Machine regression models are improved by using the low-rank matrix approximation scheme, which proves the effectiveness of the proposed method.

Laser-induced breakdown spectroscopy; Baseline correction; Asymmetric penalty; Convex optimization;PARTIAL LEAST-SQUARES; WAVELET-TRANSFORM; MODEL; LIBS; COAL

For laser-induced breakdown spectroscopy (LIBS) quantitative analysis technique, baseline correction is an essential part for the LIBS data preprocessing. As the widely existing cases, the phenomenon of baseline drift is generated by the fluctuation of laser energy, inhomogeneity of sample surfaces and the background noise, which has aroused the interest of many researchers. Most of the prevalent algorithms usually need to preset some key parameters, such as the suitable spline function and the fitting order, thus do not have adaptability. Based on the characteristics of LIBS, such as the sparsity of spectral peaks and the low-pass filtered feature of baseline, a novel baseline correction and spectral data denoising method is studied in this paper. The improved technology utilizes convex optimization scheme to form a non-parametric baseline correction model. Meanwhile, asymmetric punish function is conducted to enhance signal-noise ratio (SNR) of the LIBS signal and improve reconstruction precision. Furthermore, an efficient iterative algorithm is applied to the optimization process, so as to ensure the convergence of this algorithm. To validate the proposed method, the concentration analysis of Chromium (Cr),Manganese (Mn) and Nickel (Ni) contained in 23 certified high alloy steel samples is assessed by using quantitative models with Partial Least Squares (PLS) and Support Vector Machine (SVM). Because there is no prior knowledge of sample composition and mathematical hypothesis, compared with other methods, the method proposed in this paper has better accuracy in quantitative analysis, and fully reflects its adaptive ability. (C) 2017 Elsevier B.V. All rights reserved.