## 3 Results
### Comparative Experiments
#### 3.2.1 Dehazing Effectiveness  
Table 4 provides a detailed list of performance metrics for the model in image dehazing. The WRPM significantly outperforms other methods in terms of MSE, PSNR, and SSIM, achieving 52.3697, 30.94, and 0.9728, respectively. This indicates that the WRPM can more effectively restore image details and structural information, producing dehazing results that are closer to real haze-free images. Additionally, the LPIPS value of the WRPM is 0.0067, significantly lower than other methods, showing that its dehazed images are more perceptually close to real images with richer details. The above results show that the difference between the dehazed images generated by the WRPM and real haze-free images is the smallest. Overall, the WRPM demonstrates superior performance in dehazing compared to other methods, proving its effectiveness in handling complex hazy scenes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **MSE \(\downarrow\)** & **PSNR \(\uparrow\)** & **SSIM \(\uparrow\)** & **LPIPS \(\downarrow\)** \\ \hline DCP & 2373.0352 & 17.51 & 0.8614 & 0.0600 \\ AOD-Net & 3377.9227 & 15.10 & 0.8049 & 0.0404 \\ EMRA-Net & 2154.2254 & 18.30 & 0.8651 & 0.0466 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental results comparing dehazing effectiveness with conventional methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**Abbreviation** & **Formula** \\ \hline MSE & \(\text{MSE}=\frac{1}{mn}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}[I(i,j)-K(i,j)]^{2}\) \\ PSNR & \(\text{PSNR}=10\cdot\log_{10}\bigg{(}\frac{\text{MAX}_{1}^{2}}{\text{MSE}} \bigg{)}\) \\ SSIM & \(\text{SSIM}(x,y)=\frac{(2\mu_{x}\mu_{y}+\mathbb{C}_{1})(2\sigma_{xy}+\mathbb{C }_{2})}{(\mu_{x}^{2}+\mu_{y}^{2}+\mathbb{C}_{1})(\sigma_{x}^{2}+\mathbb{C}_{2})}\) \\ LPIPS & \(\text{LPIPS}(x,x_{0})=\sum_{l}\frac{1}{HW}\sum_{l,w}d_{l,w}^{l}\) \\ \hline \hline \end{tabular} Where \(m\) and \(n\) are the dimensions of the image, \(I(i,j)\) is the pixel value of the original image at position \((i,j)\), \(K(i,j)\) is the pixel value of the processed image at position \((i,j)\), \(\text{MAX}_{l}\) is the maximum possible pixel value of the image, \(x\) and \(y\) are two image patches being compared, and \(\mu_{x}\) and \(\mu_{y}\) are the average pixel values of \(x\) and \(y\), respectively. \(\sigma_{x}^{2}\) and \(\sigma_{y}^{2}\) are the variances of \(x\) and \(y\), respectively. \(\sigma_{xy}\) is the covariance between \(x\) and \(y\).  
\end{table} 
Table 3: _Cont._To intuitively demonstrate the effectiveness of WRFM, we show the application examples of five fog removal methods on some images in Figures 5-7. As illustrated in Figure 6, although the DCP algorithm achieves relatively thorough haze pixel removal, this comes at the expense of significant original detail loss, resulting in severe color distortion in the restored image. While AOD-Net partially alleviates the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **MSE \(\downarrow\)** & **PSNR \(\uparrow\)** & **SSIM \(\uparrow\)** & **LPIPS \(\downarrow\)** \\ \hline GCANet & 2100.5785 & 19.22 & 0.8705 & 0.0455 \\ Dehamer & 943.6245 & 19.14 & 0.8399 & 0.1202 \\ DehazeFormer & 151.7440 & 27.34 & 0.9553 & 0.0102 \\ PMNet & 181.8680 & 26.69 & 0.9194 & 0.0689 \\ WRFM & **52.3697** & **30.94** & **0.9728** & **0.0067** \\ \hline \hline \end{tabular} The best results are highlighted in bold. \(\downarrow\) means the smaller the better, \(\uparrow\) means the bigger the better.  
\end{table} 
Table 4: _Cont._  
Figure 5: The effectiveness of image dehazing, including DCP, AOD-Net, EMRA-Net, GCA-Net, Dehamer, DehazeFormer, and the WRFM. Figure 6: Comparative visualization of detail enhancement effects among DCP, AOD-Net, and the WRFM. Figure 7: Comparative visualization of detail enhancement effects among EMRA-Net, GCANet, and the WRFM. color distortion issue, it still suffers from an overall dark color cast and persistent detail loss.