改进的局部最值分段多项式拟合算法精确校正拉曼光谱基线

Improved Num-Local Piecewise Polynomial Fitting Algorithm forAccurate Correction of Raman Spectroscopy Baselines

基线校正作为拉曼光谱预处理极为关键的步骤之一,对进一步拉曼光谱数据分析和实现拉曼成像等有重要意义。目前,最常用的基线校正算法基于多项式拟合,由于其采用手动或半手动的形式,因此依赖人工经验,对用户的专业性要求较高,处理过程繁琐,处理结果差异较大。同时,在使用过程中,多项式阶数及移动分段窗口难以选择确定,因此处理的结果常出现欠拟合或过拟合现象。针对传统多项式拟合算法的此类局限性,改进了局部最值分段多项式拟合(NPPF)算法用于精确校正拉曼光谱基线。首先采用了改进的基于分段的局部最值算法,选取光谱中最宽峰底部轮廓的近似横向宽度作为背景点窗口宽度,依次选取窗口内的最小两个值作为需要拟合的背景基线点,避免直接比较或者人工选取导致的背景点选取困难,实现更准确地选取每个背景轮廓基线点。然后通过每个窗口三次拟合迭代覆盖的方式,得到三个拟合曲线函数,选取窗口内每个点对应三个曲线函数值,分别计算与前一拟合值的差值绝对值,取绝对值最小的曲线函数值作为此点拟合曲线值,从而较好地避免了传统分段多项式拟合(PPF)算法中的欠拟合和过拟合现象,同时也确定了拟合过程中的阶数和分段窗口。模拟了两种不同背景类型的拉曼光谱,将NPPF与PPF算法分别对两种模拟光谱进行处理比较,发现NPPF处理结果均方根误差(RMSE)小,证实NPPF较于PPF的优越性。最后,对实际样品(烯啶虫胺、罗丹明6G)的拉曼光谱进行了NPPF和PPF对比处理,发现NPPF的拟合基线较为准确,证实该算法NPPF在拉曼光谱基线校正预处理中具有广泛的实际应用价值和前景。

Baseline correction,one of the extremely critical steps in Raman spectroscopy pre-processing,is of great significance for further Raman spectroscopy data analysis,Raman imaging,etc.Currently,the most common baseline correction algorithm is based on polynomial fitting;due to its manual or semi-manual form,manual experience,a high level of user expertise,and a tedious processing process are required,leading to large differences in processing results.At the same time,the polynomial order and the moving segmentation window are difficult to select in the process,so the processed results are often under-fitted or over-fitted.This paper improves the Numlocal Piecewise Polynomial Fitting(NPPF)algorithm for accurately calibrating Raman spectral baselines.Firstly,an improved segmentation-based local optimum algorithm is used to select the approximate lateral width of the bottom contour of the widest peak in the spectrum as the background point window width;the minimum and second minimum values within the window,in turn,are selected as the background baseline points to be fitted,avoiding the difficulty of selecting background points,and achieving more accurate selection of each background contour baseline point.Then,the three fitted curve functions are obtained by iterative coverage of each window three times,and each point in the selected window corresponds to three curve function values,which are calculated with the previous fitted absolute value separately.The curve function value with the minimum absolute value is taken as the fitted curve value at this point.Thismethod better avoids the underfitting and overfitting phenomenon of the Piecewise Polynomial Fitting(PPF)algorithm and also determines the order and segmentation window in the fitting process.In this paper,two Raman spectra with different background types are simulated,and the NPPF and PPF algorithms are compared to process the two simulated spectra separately.The Root Mean Square Error(RMSE)of NPPF processing results is found to be smaller,which confirms the superiority of NPPF over PPF.Finally,the Raman spectra of the actual samples(alizarin and rhodamine 6G)are processed by comparing NPPF and PPF,and it is found that the fitted baseline of NPPF is more accurate,which confirms that the NPPF algorithm in this paper has wide practical application value and prospect in the baseline correction pretreatment of Raman spectra.