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

Abstract

In quantitative analysis of laser-induced breakdown spectroscopy (LIBS), 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 spectral data matrix, which is composed of different certificated samples of spectral intensity. Therefore, spectral data matrix processing is critical for LIBS quantitative analysis. A prevalent assumption of constructing matrix approximation is that the partially observed matrix is of low-rank. Moreover, the low-rank structure always reflects the useful information and can be regarded as a powerful data preprocessing method. In this paper, a novel LIBS quantitative analysis method based on a sparse low-rank matrix approximation via convex optimization is proposed. Based on the sparsity of spectral signal, we present a convex objective function consisting of a data-fidelity term and two parameterized penalty terms. To improve the accuracy of 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 is utilized to solve the optimization problem. The proposed method is applied to the quantitative analysis of 23 high alloy steel samples. Both of the performance of Partial Least Squares (PLS) and Support Vector Machine (SVM) regression model are improved by using the low-rank matrix approximation scheme, which proves the effectiveness of the proposed method.

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Publication details

The article was received on 06 May 2017, accepted on 12 Jul 2017 and first published on 12 Jul 2017


Article type: Paper
DOI: 10.1039/C7JA00178A
Citation: J. Anal. At. Spectrom., 2017, Accepted Manuscript
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    Laser induced breakdown spectroscopy quantitative analysis based on low-rank matrix approximation

    C. Yi, Y. Lv, H. Xiao and S. Tu, J. Anal. At. Spectrom., 2017, Accepted Manuscript , DOI: 10.1039/C7JA00178A

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