## 4 Results and Analysis
### Experimental Results Comparing Different Raman Spectral Denoising Algorithms  
To further validate the performance of the VMD-EWT-EBiLSTM network architecture for Raman spectral denoising, comparative experiments are conducted with four state-of-the-art denoising methods, including Fourier transform [31], Savitzky-Golay filtering [11], sliding window averaging [32], and wavelet thresholding [33].  
A Gaussian noise of 20 dB and 30 dB is added to the collected Raman spectral sequences. The prediction results are shown in Figures 9 and 10. It can be seen that for the Raman spectra with 20 dB of Gaussian noise, the denoising results for the VMD-EWT-EBiLSTM, wavelet thresholding, and sliding window averaging are consistent with the ideal Raman spectra trend, while Fourier transform and S-G filtering result in little deviation from the ideal values. As the noise increases, processing Raman spectra with 30 dB of Gaussian noise, the denoising effects of sliding window averaging and wavelet thresholding fluctuate more, with some deviation around the peaks compared to the ideal spectrum. Fourier transform and Savitzky-Golay filtering do not provide satisfactory denoising effects. The VMD-EWT-EBiLSTM used in this paper maintains stable denoising performance.  
Objective metrics on the signal-to-noise ratio (SNR) and mean squared error (MSE) are further utilized to evaluate the performance of different denoising methods. The specific results are shown in Table 3. It can be intuitively seen that the denoising model proposed in this paper has relatively lower errors. Compared to existing mainstream prediction algorithms, the denoising performance is improved by 13.38% to 72%, better demonstrating the superior denoising effects of the VMD-EWT-EBiLSTM network architecture on Raman spectral curves.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Raman Spectral**} & \multirow{2}{*}{**EMD**} & \multirow{2}{*}{**VMD**} & \multirow{2}{*}{**EBiLSTM**} & \multicolumn{1}{c}{**VMD-EWT-EBiLSTM**} \\  & & **Sequence with Noise** & & & & **EBiLSTM** & **EBiLSTM** \\ \hline \multirow{3}{*}{20 dB} & MSE & 14.5969 & 5.7591 & 3.8723 & 3.2742 & 2.5137 \\  & SNR & 11.7945 & 15.7468 & 20.3494 & 23.6497 & 26.1491 \\ \cline{1-1}  & MSE & 24.1763 & 9.4766 & 5.6714 & 3.7818 & 2.9173 \\ \cline{1-1}  & SNR & 4.6342 & 10.3823 & 14.1918 & 18.6463 & 24.7691 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of various decomposition methods for MSE and SNR.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & **Raman Spectral** & **Fourier** & **Sliding Window** & **Savitzky-** & **Wavelet** & **VMD-EWT-** \\  & & **Sequence with Noise** & **Transform** & **Averaging** & **Golay** & **Thresholding** & **EBiLSTM** \\ \hline \multirow{2}{*}{20 dB} & MSE & 15.1737 & 8.3794 & 2.9908 & 6.3724 & 2.6177 & 2.1164 \\  & SNR & 8.4739 & 14.4940 & 21.8077 & 18.7647 & 22.0222 & 24.9691 \\ \hline \multirow{2}{*}{30 dB} & MSE & 29.3914 & 16.8756 & 6.1258 & 13.0745 & 4.1837 & 3.2727 \\  & SNR & 4.7192 & 8.3827 & 13.4691 & 10.7281 & 16.6238 & 20.7194 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of various denoising methods for MSE and SNR.