用于光谱重叠峰和太赫兹波时域曲线的高斯拟合算法  

Gaussian Fitting Algorithm for Spectral Overlapping Peaks and Terahertz Time-Domain Curves

作　　者：杨家懿 熊永前 Yang Jiayi;Xiong Yongqian(State Key Laboratory of Advanced Electromagnetic Engineering and Technology,School of Electrical and Electronic Engineering,Huazhong University of Science and Technology,Wuhan,Hubei 430074,China)

机构地区：[1]华中科技大学电气与电子工程学院强电磁工程与新技术国家重点实验室,湖北武汉430074

出　　处：《激光与光电子学进展》2021年第4期71-77,共7页Laser & Optoelectronics Progress

摘　　要：为了拟合光谱重叠峰及太赫兹时域曲线,设计了一种动态增加高斯函数的高斯拟合算法。首先,利用去噪光谱数据的一阶导数粗略搜寻各高斯峰的位置,再根据高斯峰位置初始化多高斯函数。然后,将光谱数据与多高斯函数的均方差作为损失函数,用梯度下降法找到损失函数最小时的多高斯函数。最后,针对没有明显峰尖的光谱重叠峰和存在负值的太赫兹时域曲线,用动态多高斯函数模型解析重叠高斯峰或拟合曲线。计算结果表明,本算法可以根据拟合精度的要求,动态增加多个高斯函数,自动搜寻高斯峰的位置,且对光谱重叠峰和太赫兹时域曲线的拟合效果较好。In order to fit the spectral overlapping peaks and terahertz time-domain curves,a Gaussian fitting algorithm that dynamically increases the Gaussian function is designed in this paper.First,use the first derivative of the denoising spectral data to roughly search the position of each Gaussian peak,and then initialize the multi-Gaussian function according to the position of the Gaussian peak.Then,the mean square error between the spectral data and the multi-Gaussian function is used as the loss function,and the gradient descent method is used to find the multi-Gaussian function when the loss function is the smallest.Finally,for the spectral overlapping peaks without obvious peaks and the terahertz time-domain curves with negative values,the dynamic multi-Gaussian function model is used to analyze overlapping Gaussian peaks or fitting curves.Calculation results show that the algorithm can dynamically add multi-Gaussian functions according to the requirements of fitting accuracy,and automatically search for the position of Gaussian peaks,and the effect of fitting spectral overlapping peaks and terahertz time-domain curves is better.

关 键 词：光谱学 太赫兹时域曲线 高斯曲线拟合 自动寻峰算法 梯度下降法 

分 类 号：TN911.74[电子电信—通信与信息系统]