Sparse Convex Optimization Theory And Its Application On Quantitative Analysis Of Laser Induced Breakdown Spectroscopy

Laser-induced breakdown spectroscopy is a new testing technology for the rapid detection and elemental analysis of material components,it has the advantages of rapid analysis,no need for complex sample processing,simultaneous analysis of multiple elements.The technology of laser-induced breakdown spectroscopy includes the data collection,processing,and subsequent quantitative analysis of spectroscopic spectral data to determine the composition and content of the material,among them,the quality of spectral data preprocessing determines to the result of quantitative analysis of elements accuracy.In general,the LIBS signal mainly consists of characteristic peaks,background and noise.The characteristic peaks have typical characteristics of sparseness,the background or the baseline has the characteristics of low frequency,and the noise has the characteristics of high frequency and randomness.Therefore,according to the characteristics of LIBS signal,the spectral signal are processed to improve the accuracy of quantitative analysis by using sparse convex optimization theory.The main research of this paper are as follows:1.Spectral signal noise is characterized by high frequency and randomness,and characteristic peaks are sparse.This paper proposes a new class of non-convex penalty functions that is a multivariate generalization of the minimax-concave penalty.It is a new multivariate extension to the Huber function,it achieves sparse representation of spectral data and noise reduction processing.After using the algorithm proposed in this topic to denoise the spectral signal,the high-frequency random noise in the LIBS can be removed.2.Aiming at the influence of baseline drift in LIBS quantitative analysis,due to the obvious independence and sparsity of the characteristic peaks of the spectral signal,and the baseline is a low-pass signal.this paper proposes a baseline correction method based on the convex optimization theory,an exponential penalty function is used instead of the logarithmic penalty function.This project uses the baseline corrected spectra for quantitative analysis and shows the usefulness of the proposed method.3.Existing standard-based regression models have poor precision in quantitative analysis of LIBS.To solve this problem,we proposes an improved random forest regression model and it applies to LIBS quantitative analysis.It combines the idea of low-rank matrix approximation in the convex optimization theory with the random forest model,it improves LIBS quantitative analysis accuracy.The advantages of this method in quantitative analysis are verified by comparing with partial least squares and support vector machine models.