在利用表面增强拉曼光谱(SERS)对毛发中痕量物质进行分析时, 该SERS信号中毛发特征峰与增强基底背景峰会相互耦合。 在耦合情况下, 背景峰会被误识别为毛发特征峰, 导致待测物的识别错误, 此外具有高峰强特性的背景峰对毛发中微弱特征峰产生掩盖干扰。 因此, 背景峰的扣除是解决上述问题的重要途径, 但常规的扣峰方法会导致周围邻峰的严重失真。 针对上述问题提出了高斯混合模型, 该模型在表征SERS信号的同时又使得各特征峰相互独立, 在扣峰过程中对周围邻峰不产生干扰, 既实现干扰峰的扣除又保证了邻峰的微失真。 高斯混合模型的核心问题在于模型参数的求解, 文中提出了小波变换与共轭梯度法, 分别解决模型的初始参数问题及最优解问题。 小波变换通过映射放大SERS信号的细节信息, 充分提取该信号的细微特征信息, 将该特征信息作为模型的初始参数。 其中共轭梯度法是迭代优化方法, 将模型参数进行循环迭代优化, 最终收敛结果即为模型参数的最优解。 综上两种方法可准确建立高斯混合模型, 模型中单高斯函数为SERS信号的特征峰, 且两者的峰形保持一致。 在扣除SERS信号的背景峰时应遵循以下过程, 包括有效数据的提取、 模型建立和峰的扣除。 其中有效数据的提取是对空白与滴样的增强基底进行同位置检测, 由此得到一组SERS信号。 模型建立是通过高斯混合模型对滴样SERS信号进行表征, 该信号可由多个高斯函数表现。 最后利用空白增强基底的特征峰对滴样的SERS信号进行指认, 其中峰形相似且峰位相同的特征峰可扣除。 实验结果表明, 方差值比最小时, 高斯混合模型的峰位、 峰宽、 峰强等特征与毛发SERS信号基本相同, 此时高斯混合模型可准确表征毛发SERS信号的特征信息。 在对7组毛发进行扣峰实验时, 毛发SERS信号中背景峰扣除率达到50%～100%, 同时毛发的特征峰也得到有效提取。 在对真实毛发样本进行快速分析时, 该模型识别出了毒品曲马多。

In the analysis of trace substances in hair by Surface-Enhanced Raman Spectroscopy (SERS), the characteristic peaks of hair are coupled with the background peaks of the substrate. In the case of coupling, the background peaks are mistakenly identified as the characteristic peak of hair, resulting in the identification error of the analyte to be tested. In addition, the strong background peak has a masking interference on the weak characteristic peak in hair. Therefore, the background peak deduction is an important way to solve the above problems. However, the conventional peak deduction method always leads to serious distortion of the surrounding peaks. In this paper, a Gaussian mixture model is proposed. The model not only characterizes the SERS signal but also makes each characteristic peak independent of the other, and does not interfere with the adjacent peaks in the process of peak deduction, which realizes the deduction of interference peaks and ensures the micro distortion of adjacent peaks. The core problem of the Gaussian mixture model is the solution of model parameters. In this paper, wavelet transform and conjugate gradient methods are proposed to solve the model’s initial parameter problem and optimal solution problem. The wavelet transforms fully extracts the subtle feature information of the signal by mapping the detailed information of the amplified SERS signal and takes the feature information as the initial parameter of the model. The conjugate gradient method is an iterative optimization method, and the model parameters are iteratively optimized. The final convergence result is the optimal solution of the model parameters. In summary, the two methods can accurately establish the Gaussian mixture model, and the single Gaussian function is the characteristic peak of the SERS signal, and the peak shape of the two methods is consistent. The deduction of background peak should include the extraction of effective data, model establishment, and peak deduction. The effective data extraction is to detect the blank and sampled substrate in the same position, thus obtaining a set of SERS signals. The model was established to characterize the SERS signal of the sampled substrate by the Gaussian mixture model, which multiple Gaussian functions can express. Finally, the SERS signal of the sampled substrate was identified by the characteristic peaks of the blank substrate, and the characteristic peaks with similar peak shapes and the same peak position can be deducted. The results show that when the variance ratio is the smallest, the peak position, peak width, and peak intensity of the Gaussian mixture model are the same as those of the hair SERS signal. At this time, the Gaussian mixture model can accurately characterize the information of SERS signal of hair. In seven groups of hair peak deduction experiments, of the hair SERS signal background peak deduction rate reached 50%~100%, while the hair characteristic peak wasalso effectively extracted. The model was used to identify tramadol in the rapid analysis of real hair samples.