Abstract：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.
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