# PMT Fluorescence Signal Denoising Processing Based on Wavelet Transform and BP Neural Network
## 3 Wavelet Transform  
Due to sulfur dioxide being a trace gas in the atmosphere, the number of fluorescent photons generated by excitation is very small, making it susceptible to interference from electronic noise. Therefore, noise reduction processing is the key to improving the accuracy of equipment detection. Figure 3: Collect physical circuit diagram. Figure 2: Subtraction circuit diagram. Wavelet transform [25; 26] is a powerful signal processing tool and a mathematical method widely used in various fields such as signal processing and seismic exploration. It decomposes and analyzes signals at different scales and positions using wavelet functions. Before reaching the optimal decomposition level of the signal, the relationship between signal-to-noise ratio and decomposition level is expressed as an approximate positive correlation. After reaching the optimal decomposition level, the signal-to-noise ratio of the signal will not increase again but will instead decrease. Applying threshold denoising techniques to each sub band [27] can effectively remove noise and preserve the true signal. The MATLAB multi-resolution analysis is an important tool for wavelet transform analysis. In order to distinguish effective signals from noisy signals, a series of detail signals with different resolutions can be used for hierarchical representation. The process of wavelet decomposition is shown in Figure 4.  
In this fluorescence detection system, the effective signal is usually a low-frequency signal, while electronic noise is usually a high-frequency signal. Therefore, the original signal can be decomposed a certain number of times through wavelet transform to isolate the effective signal from noise, thereby removing the interference of high-frequency electronic noise and improving the signal-to-noise ratio. The wavelet transform denoising used in this article can be divided into the following three steps:  
(1) Original signal decomposition. Firstly, select multiple original signals, perform N-layer wavelet decomposition on the signals, identify common trends in the signals, and modify and compare the parameters. (2) Noise signal removal. Adjust and optimize the high-frequency noise threshold coefficients for each layer from layer 1 to layer N, and select the optimal noise reduction coefficient to reduce the impact of electronic noise. (3) Effective signal reconstruction. Perform wavelet reconstruction of fluorescence signals based on the low-frequency coefficients of the Nth layer of wavelet decomposition and the high-frequency coefficients of the 1 st to Nth layers after quantization processing. The most crucial step in these three steps is the determination of the threshold, which aims to remove electronic noise as much as possible while ensuring that the effective signal is not distorted. Due to the discontinuity of the hard threshold function at the selected threshold, it can cause system oscillations and cause distortion. A soft threshold will cause some singularities to disappear [28; 29], resulting in the loss of key details of the signal, so this paper proposes an improved threshold wavelet decomposition algorithm for this experimental environment. The collection of fluorescent signals faces noise problems, mainly due to the following reasons:  
(1) The signal itself is weak. Due to the concentration of sulfur dioxide in this experiment being at the ppb level, the excited fluorescence signal is very weak. If not properly processed, such a signal is easily masked by other noise. (2) Device noise. Electronic components usually introduce a certain degree of noise, such as operational amplifiers, filters, voltage stabilizing chips, etc. These noises may come  
Figure 4: Wavelet denoising process. from the internal circuits of the device or from the interaction between the device and the external electromagnetic environment. (3) Environmental noise. There may be various sources of interference in the experimental environment, such as power crosstalk, electromagnetic radiation, thermal noise, etc.