# A Shearlets-Based Method for Rain Removal from Single Images
## 5 Numerical Experiments
### Comparison Tests of the Synthetic Data  
The testing results and discussions for synthetic data are given in this subsection. First, the synthetic rainy image is generated as follows: (1) adding the salt and pepper noise with a random density _den_ (which decides the density of rain streaks) to a zero matrix; (2) convoluting (1) with a motion kernel (including the directional parameter \(\theta\) and motion parameter _len_); (3) adding (2) to the rain-free images to obtain the rainy image [14]. The parameters of synthetic rainy image for testing are given in Table 1. Then these RGB rainy images are converted to YUV channels, and only the rain streaks in the Y channel are removed using the 15 ICCV method, the 16 CVPR method, the 18 UTV method, and the proposed method. In this test, we choose 5 images as the testing images, which can be downloaded from the dataset \"UCID\" ([[http://homepages.lboro.ac.uk/cgs/datasets/ucid/ucid.html](http://homepages.lboro.ac.uk/cgs/datasets/ucid/ucid.html)]([http://homepages.lboro.ac.uk/cgs/datasets/ucid/ucid.html](http://homepages.lboro.ac.uk/cgs/datasets/ucid/ucid.html))) and ([[https://pixabay.com/](https://pixabay.com/)]([https://pixabay.com/](https://pixabay.com/))). The testing image are given in Figure 4. The visual results for 4 methods are displayed in Figure 5. The first column displays the de-rain results by the 15 ICCV method, the second column shows the de-rain results by the 16 CVPR method, the third column gives the de-rain results by the 18 UTV method, and the last column shows the de-rain results by the proposed method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & _den_ & _len_ & \(\theta^{\circ}\) \\ \hline
1 & [0.02, 0.04, 0.06, 0.08] & 10 & 30 \\
2 & 0.04 & [10, 20, 30, 40] & 15 \\
3 & 0.04 & 10 & [\(-15\), \(-5\), \(0\), \(5\), \(15\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters list. From Figure 5 and the corresponding zooming in images in Figure 6, we find that the method 15 ICCV fails to remove the rain streak completely, which leads to the lower SSIM value, and while methods 16 CVPR and 18 UTV perform better than 15 ICCV, they cannot outperform our method. Comparing with three methods, the proposed method removes rain streaks and preserves the details of the background layer more efficiently. Then we have the conclusion as follows:  
* the method 15 ICCV cannot remove rain streaks completely, especially with heavy rain;  
Figure 4: The ground truth and rainy image of synthetic testing images. Figure 5: The visual results of four methods for synthetic images. * the method 16 CVPR does remove rain streaks completely, but the resulted background seems to be over-smooth;
* the method 18 UTV can remove rain streaks completely, but rain streaks are detected by TV, which leads to a non-smooth background, especially in the heavy rain case;
* the proposed method using multilevel system performs better both in rain streaks removal and details preservation in heavy and light rain cases. The quantitative results for different methods with different rain streaks' direction are presented in Table 2, including PSNR, SSIM, and RelErr values for both the background layer and the rain streak layer in heavy and light rain cases. In addition, we randomly choose 20 images from UCID dataset to further test the rain removal performance in different directional rainy images.