## 3 The Proposed Method
### A Raman Spectral Denoising Model Using Vmd-Ewt-EbiLSTM  
To improve the denoising accuracy of Raman spectra, this paper proposes a Raman denoising model based on VMD, EWT, and EBiLSTM modules. The prediction flowchart of the model is shown in Figure 2 below. The signal components decomposed from the original signal by VMD are called intrinsic mode functions, abbreviated as IMF.  
First, VMD is utilized to decompose the original Raman spectral sequence into several sub-sequences and a residual sequence. EWT is then used to further decompose the residual sequence. The sub-sequences from the VMD decomposition are categorized into spectral signals and noise signals using the zero-crossing rate and correlation coefficient. The zero-crossing rate [24] is specifically defined as:  
\[Z_{0}=\frac{z_{0}}{N} \tag{12}\]  
In Equation (12): \(Z_{0}\) denotes the zero-crossing rate, \(z_{0}\) is the number of zero crossings, \(N\) is the total number of load samples.  
The correlation coefficient [25] between the modal sequences from the VMD decomposition and the original signal is calculated as specifically defined below:  
\[coor=\frac{\sum\limits_{i=1}^{n}{(x_{i}-\overline{x})(v_{i}-\overline{v})}}{ \sqrt{\sum\limits_{i=1}^{n}{(x_{i}-\overline{x})^{2}\sum\limits_{i=1}^{n}{(v_ {i}-\overline{v})^{2}}}}} \tag{13}\]  
where: \(x\) represents the original signal, \(v\) represents the modal sequence.  
Next, the categorized spectral signal sub-sequences are input into a network structure with a small number of stacked EBiLSTM modules, termed EBiLSTM_Low, to capture the long-term dependencies of the spectral sequence features and extract the features with low noise interference. The categorized noise sequences are input into a stack of high-frequency EBiLSTM modules, termed EBiLSTM_High, for further feature extraction and noise identification to eliminate additional noise. Finally, the signal and noise identification results for each sub-sequence are superimposed to reconstruct the overall denoised spectral result.  
The designed Raman spectral prediction model based on VMD-EWT-EBiLSTM is illustrated in Figure 3. The backbone network for the spectral signal components captures the feature temporal correlations and extracts information through stacked EBiLSTM modules, with 1, 2, 4, 2 layers stacked. The backbone network for the noise signals extracts local Raman spectral features and noise signals through high-frequency stacked IASSP  
Figure 2: Raman denoising prediction process flowchart.  
structures with 2, 2, 2, 4, 4, 2 modules stacked, jointly forming a dual-channel spectral signal and noise feature extraction and denoising model. The extracted feature information from the dual-channel links is superimposed for reconstruction, and input into 64 short-term and long-term neural structures to learn the fused features and noise characteristics from both paths. The features captured by the short-term and long-term neurons are then connected through a skip structure. After concat layer processing, it is input into the fully connected layer, and dropout layers are utilized to avoid overfitting. Finally, spectral signal and interference noise discrimination is performed through a sigmoid activation function.