## 4 Experiments
### Comparison Experiments
#### 4.5.2 Results on Synthetic Datasets  
To confirm the efficacy and advancements of the suggested algorithm, we evaluated it against a number of cutting-edge deraining algorithms. The compared algorithms include supervised deraining algorithms such as DARAGNet [34], DSMNet [35], IDT [36], and RCHNet [37], as well as semi-supervised deraining algorithms like MOSS [15], LSNet [17], and SSID_KD [38]. For fair comparison, all the compared algorithms were retrained and tested on the artificial datasets Rain1200 and Rain1400. The test outcomes were recalculated using PSNR and SSIM values in Matlab as evaluation metrics, where larger values indicate better results. 1. Quantitative Comparison  
The quantitative findings for the Rain1200 dataset are displayed in Table 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Frequency**} & \multicolumn{2}{c}{**Rain1200**} & \multicolumn{2}{c}{**Rain1400**} & \multicolumn{2}{c}{**RealRain**} \\ \cline{2-7}  & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **NIQE** & **PIQE** \\ \hline FFT & 33.36 & 0.944 & 32.10 & 0.936 & 13.20 & 10.40 \\ DCT & 33.28 & 0.940 & 32.05 & 0.930 & 13.11 & 10.29 \\
**MSWT** & **34.86** & **0.961** & **32.55** & **0.953** & **11.52** & **9.13** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of three frequency-based methods on synthetic and real datasets. (The bold words indicate the experimental results of the algorithm proposed in this paper.) \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Comparison Algorithms**} & \multicolumn{2}{c}{**Rain1200**} & \multicolumn{2}{c}{**Rain1400**} \\ \cline{2-5}  & **PSNR** & **SSIM** & **PSNR** & **SSIM** \\ \hline DARAGNet & 32.68 & 0.890 & 31.44 & 0.885 \\ DSMNet & 32.93 & 0.891 & 31.67 & 0.923 \\ IDT & 33.88 & 0.893 & 32.12 & 0.890 \\ RCHNet & 34.04 & 0.912 & **32.58** & **0.955** \\ MOSS & 34.15 & 0.927 & 32.25 & 0.906 \\ LSNet & 34.37 & 0.930 & 32.46 & 0.927 \\ SSID\_KD & 34.53 & 0.944 & 32.38 & 0.923 \\ MSWT-SSIDA & **34.86** & **0.961** & 32.55 & 0.953 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Quantitative results of different algorithms on synthetic dataset. (Highlight the best and second best results in bold and underlined). From Table 5, It is evident that, on the Rain1200 dataset, the suggested method performs better than the semi-supervised SSID_KD algorithm, with a PSNR enhancement of 0.33 dB and an SSIM enhancement of 0.017, achieving the best values. On the Rain1400 dataset, the proposed algorithm shows improvements in PSNR and SSIM in contrast to most other algorithms, and is second only to RCHNet, a supervised learning-based method, in achieving the best PSNR and SSIM values. 2. Qualitative Comparison  
Figure 12 shows the deraining results on the Rain1200 dataset, where rain streaks are relatively simple. All algorithms effectively removed the rain streaks, but some showed residual streaks or distortions. DARAGNet, DSMNet, and IDT left streaks in the edge details, while RCHNet caused slight color distortions in the background. Semi-supervised methods like MOSS and LSNet removed rain but blurred the background, while SSID_KD and the proposed algorithm successfully removed rain while preserving background details. The deraining findings on the Rain1400 statistics are displayed in Figure 13. For this more complex dataset, where the rain streak intensity and rain scenes are more complex, Figure 13 shows that supervised algorithms like DARAGNet, DSMNet, and IDT leave small residual rain streaks in the background, while MOSS shows some flaws in the background. The semi-supervised algorithms LSNet and SSID_KD still show residual rain streaks, which affect the image's visual quality to varying degrees. In contrast, both RCHNet and the proposed algorithm deliver better deraining results while preserving background details. Figure 12: Comparison of results of different algorithms on the Rain1200 dataset.