# Rain Removal of Single Image Based on Directional Gradient Priors
## 4 Experiments
### Experiments on Simulated Sets  
To compare these methods fairly, 10 test images are selected from the published dataset [14], which are widely accepted and used by most researchers engaged in image rain removal. To prove the validity of the sparse directional gradient regularization terms proposed in this paper, we carried out ablation experiments for different models to obtain the rain removal results. The objective indexes of the results of the different models are shown in Table 1. In Table 1, the original model contains only the first and second items of Equation (4), namely Model 1. Model 2 indicates that two gradient priors, \(||\
abla_{y}R||_{1}\) and \(||\
abla_{x}R||_{1}\), are added to the original model. Model 3 is a model that removes two gradient priors on the basis of Formula (4) and utilizes multiscale dictionaries to reconstruct the rain layer in the model. Our model refers to the model of Equation (4). The four groups of data in Table 1 represent the average values of the PSNR and SSIM of the rain removal results obtained by executing four models on the 10 test images. It can be seen from Table 1 that the PSNR and SSIM values obtained by Model 2 with a gradient prior and Model 3 with multi-scale dictionaries are higher than those obtained by the original model. Our model with two gradient priors and multi-scale dictionaries achieves the highest evaluation indexes in all the models. As a result, our model can obtain better rain removal results. To further evaluate the performance of the proposed model, we illustrate the average values of the PSNR and SSIM of the rain removal results obtai \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **Model 1** & **Model 2** & **Model 3** & **Model 4** \\ \hline Original & ✓ & ✓ & ✓ & ✓ \\ Two Priors & x & ✓ & x & ✓ \\ Multi-Scale & x & x & ✓ & ✓ \\ PSNR/SSIM & 31.92/0.9206 & 32.18/0.9220 & 32.35/0.9298 & 33.72/0.9408 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PSNR (dB)/SSIM Results of Images after Rain Removal by Different Models. Figure 5: The average PSNR of different \(a_{0}\) values on the exponential function. parison methods on 10 test images, as shown in Table 2. The best indicators are marked in red and bold, and the second-best indicators are underlined. As can be seen from Table 2, the proposed algorithm in this study obtains the highest average PSNR and SSIM values. Compared with the other methods, the proposed method obtains higher PSNR and SSIM values on 10 test images, most of which are the highest and a few are the second highest. This shows that the proposed method is superior to the other comparison methods in terms of objective evaluation. The subjective effects of the synthetic experiments are shown in Figures 6 and 7. Owing to the repeated use of guided filtering, the rain removal images obtained by the GF are more blurred and the details in the image are seriously lost. The results obtained by the GMM method still have residual information of the rain streaks and have the loss of the edge information. For example, there are obvious streaks in the sky area in Figure 6c, and Figure 7c also shows that the edges of the image are obviously blurred. Compared with the previous methods, the JCAS method retains more texture information of the original image and obtains a better rain removal image. However, there is still a small amount of rain streaks in the image, and there are also obvious artifacts, particularly in the high-frequency details of the image, such as the \"bamboo\" area in Figure 7e. The rain removal images obtained by DetailsNet, as shown in Figures 6f and 7f, have a high structural similarity with the ground truth (rainless image), but there is also an obvious color distortion, such that the color of the image is brighter than that of the ground truth. The results obtained by the LPNet method have obvious noise and artifacts, and the structural details of the image are lost, as can be observed in Figure 7g.