改进LMS的光谱信号去噪算法

Spectral Signal Denoising Algorithm Based on Improved LMS

微型光谱仪在检测高浓度比背景下多种痕量重金属离子浓度时,光谱吸收信号易受外部环境和内部电路的随机噪声干扰,多种痕量重金属离子的光谱吸收信号微弱易被噪声所淹没,严重影响了光谱定量分析结果的准确性和重复性,需要对光谱吸收信号进行去噪预处理。然而,大多数光谱去噪算法的一些关键细节参数的设置不仅需要通过反复的实验进行测试验证,还取决于研究者的现有经验和待解决对象的特征。针对这些关键参数对滤波效果影响大、选择难的问题,提出了一种基于sigmoid误差约束的改进型LMS自适应去噪算法。首先对标准LMS算法原理进行了分析,并结合微型光谱仪的数据干扰情况对标准LMS算法的滤波器结构进行优化改进,利用sigmoid函数具有误差约束的特性,对标准LMS算法的误差计算模块进行优化改进,降低算法对噪声敏感性;然后针对改进后的最小均方误差损失函数是一个非凸函数,提出了一种类交叉熵损失函数,将非凸问题转化为一个凸优化问题,在利用梯度下降法逐步最小化损失函数时,保证了局部最优解也是全局最优解,同时结合Adam算法来自适应地调整学习率因子,保证了算法具有较快的收敛速度;最后为了验证改进后的自适应去噪算法具有较强的去噪性能,通过交叉验证进行实验验证。对四种金属离子混合溶液的实测光谱吸收信号,添加不同信噪比的随机噪声后使用该改进的算法进行测试验证,实验结果表明:在处理信噪比低的吸收光谱信号过程中,所提方法相对于标准LMS算法、SG去噪算法、小波软阈值算法、小波硬阈值算法,信噪比分别提高了9.225%,19.678%,7.591%和12.042%;均方误差分别降低了59.647%,63.070%,53.600%和57.793%。该方法不仅能够有效地抑制强噪声,还原了光谱信号中的一些重要真实细节特征,而且也避免了关键细节参数需要依靠主观判断选择的问题,为分析低信噪比下的光谱信号提供了一种新的解决思路。

Under the high ratio of concentration,the spectral absorption signals detected by micro-spectrometer are easily disturbed by external environment and internal circuit noise.The spectral absorption signals of trace multi-metal ions are also weak and easily masked by noise,which seriously affects the accuracy and repeatability of the results of spectral quantitative analysis.Therefore,denoising of spectral absorption signal is required.However,the selection of some key detail parameters of most denoising algorithms not only needs to be tested and verified by repeated experiments,but also depends on the experience of the researchers’experience and the characteristics of the signals.In view of the problem that these key parameters have great influence on filtering and are difficult to select,an improved LMS adaptive denoising algorithm based on sigmoid error constraints is proposed in this paper.Firstly,the principle of standard LMS algorithm is analyzed,and the standard LMS filter structure is optimized and improved in combination with the data interference of the micro spectrometer.Meanwhile,due to the characteristics with error constraints,the sigmoid function is used to optimize the error calculation module,reducing the algorithm sensitivity of noise.Then,for the improved least mean square error loss function is a nonconvex function,this paper proposes a kind of cross-entropy loss function,which transforms the nonconvex problem into a convex optimization problem.When using the gradient descent method to gradually minimize the loss function,it ensures that the local optimal solution is also the global optimal solution.The Adam algorithm is also used to adaptively adjust the learning rate factor,which ensures the fast convergence speed of the algorithm.Finally,in order to verify that the improved adaptive denoising algorithm has strong denoising performance,the proposed method is verified by cross-validation.The measured spectral absorption signals of four kinds of multi-metal ion mixed are used to test the performance of the proposed denoising method.The experimental results show thatwhen processing absorption spectrum signals with low signal-to-noise ratio(SNR),compared with the standard LMS algorithm,SG denoising algorithm,wavelet soft threshold algorithm and wavelet hard threshold algorithm,the SNR of the proposed method is increased by 9.225%,19.678%,7.591%,12.042%,respectively,the mean square error of the proposed method is reduced by 59.647%,63.070%,53.600%,57.793%.The proposed method can not only effectively remove the influence of irrelevant noise,but also retain some important detail features in the spectral signal,and avoid the subjective selection of parameters.In conclusion,it provides a new solution to analyze the spectral signal of low SNR.