## 4 Experiments and Results
### Quantitative and Qualitative Results on The Synthetic Images  
In this paper, the proposed model was evaluated using subjective and objective evaluations. The peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were used for the objective evaluation of the dehazing effect [56]. A larger value of PSNR indicated a better dehazing effect, while the value of SSIM was in the range [0, 1], where a closer value to 1 indicated a better dehazing effect. Given a clear image \(Y\) and the corresponding haze-free image \(\hat{Y}\) after dehazing, the PSNR formula is shown in Equation (12), where MSE denotes the mean-square-error between \(Y\) and \(\hat{Y}\) and \(n\) denotes the number of bits of pixels. \[PSNR=10 log_{10}\left(\frac{\left(2^{n}-1\right)^{2}}{MSE}\right). \tag{12}\]  
The SSIM metric measures the similarity of images in terms of brightness, contrast, and structure. It is calculated as shown in Equation (13), where \(\mu_{x}\) and \(\mu_{y}\) are the mean values of image \(x\) and image \(y\), respectively, \(\sigma_{x}\) and \(\sigma_{y}\) are the standard deviations of image \(x\) and image \(y\), respectively, and \(\sigma_{xy}\) is the covariance of image \(x\) and image \(y\). \[SSIM(x,y)=\frac{\left(2\mu_{x}\mu_{y}+c_{1}\right)\left(2\sigma_{xy}+c_{2} \right)}{\left(\mu_{x}^{2}+\mu_{y}^{2}+c_{1}\right)\left(\sigma_{x}^{2}+ \sigma_{y}^{2}+c_{2}\right)}. \tag{13}\]  
To verify the effectiveness of the algorithm in this paper, we used the algorithm in this paper to compare with classical traditional image-dehazing algorithms and deep-learning-based image-dehazing algorithms, including DCP [36], AOD-Net [14], GCANet [44], EPDN [57], and YOLY [58]. As can be seen from Table 3, the PSNR and SSIM metrics obtained by the proposed method in this paper on the SOTS test set were higher than those of several other algorithms. Compared with GCANet, the PSNR and SSIM metrics were improved by 2.54 and 0.048, respectively. Figure 8 shows some of the haze-free images obtained by the algorithm in this paper and several other algorithms on the SOTS test set. As shown in Figure 8, the haze image obtained by the DCP algorithm had a very serious color distortion problem, and the overall color was brighter, which is not suitable for dehazing high-brightness areas. The haze image obtained by the AOD-Net algorithm still had a small amount of haze residue, which led to a slight decrease in the overall brightness of the image. The GCANet algorithm could remove the haze in the image well, but caused image details to be mutilated. The EPDN algorithm caused some details of the haze image to be unclear. The YOLY algorithm obtained a haze image with partial color distortion. The proposed algorithm in this paper showed a better dehazing effect without color distortion, and it could better preserve the color and texture of the image, making the color and details of the haze-free image closer to those of the real image, and making the haze-free image better in terms of visual effects, improving the dehazing effect in both qualitative and quantitative aspects. In addition, as can be seen from the fourth column of Table 3, compared with other methods, the proposed method in this paper not only improved the dehazing effect, but also increased the number of model parameters, meaning that the amount of calculation was increased. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **PSNR** & **SSIM** & **Param** \\ \hline DCP & 18.38 & 0.819 & - \\ AOD-Net & 20.08 & 0.861 & 0.002M \\ GCANet & 21.66 & 0.867 & 0.70M \\ EPDN & 22.57 & 0.863 & 17.38M \\ YOLY & 20.39 & 0.889 & 13.49M \\ Ours & **24.20** & **0.916** & 96.15M \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative results on the SOTS. As can be seen from Table 4, the PSNR and SSIM metrics obtained by the method proposed in this paper on the HSTS test set were higher than those of several other algorithms. Compared with GCANet, PSNR and SSIM were improved by 2.69 and 0.038, respectively.