# Frequency-Based Haze and Rain Removal Network (FHRR-Net) with Deep Convolutional Encoder-Decoder
## 4 Conclusions  
Rain and haze are significant obstacles to camera-based vision systems because of the degraded input image. In real-world road conditions, not only good weather but also hazy and rainy weather exist, which can cause serious visual problems. Many studies have been  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **Average PSNR** & **Average SSIM** \\ \hline Without frequency-based method & \(\mu=21.02\), \(\sigma^{2}=1.55\) & \(\mu=0.82\), \(\sigma^{2}=0.08\) \\ FHRR-Net & \(\mu=22.02\), \(\sigma^{2}=1.20\) & \(\mu=0.91\), \(\sigma^{2}=0.06\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Experimental results on frequency-based method effects.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Without** & **Without** & **FHRR-Net** \\  & **Dilated Convolution** & **Negative Mapping** & \\ \hline Average PSNR & \(\mu=21.582\), \(\sigma^{2}=1.15\) & \(\mu=21.96\), \(\sigma^{2}=1.23\) & \(\mu=22.02\), \(\sigma^{2}=1.20\) \\ \hline Average SSIM & \(\mu=0.88\), \(\sigma^{2}=0.06\) & \(\mu=0.89\), \(\sigma^{2}=0.07\) & \(\mu=0.91\), \(\sigma^{2}=0.06\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average PSNR and SSIM with different structures on the synthesized dataset.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Darkest** & **Darkest** & **Darkest** & **Darkest** \\
**0.05\% Pixel** & **0.1\% Pixel** & **0.15\% Pixel** & **0.2\% Pixel** \\ \hline Average PSNR & \(\mu=21.96\), \(\sigma^{2}=1.21\) & \(\mu=22.02\), \(\sigma^{2}=1.22\) & \(\mu=22.00\), \(\sigma^{2}=1.23\) & \(\mu=21.94\), \(\sigma^{2}=1.20\) \\ \hline Average SSIM & \(\mu=0.9105\), \(\sigma^{2}=0.0617\) & \(\mu=0.9105\), \(\sigma^{2}=0.0616\) & \(\mu=0.9105\), \(\sigma^{2}=0.0617\) & \(\mu=0.9103\), \(\sigma^{2}=0.0612\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average PSNR and SSIM for each threshold to determine A.  
conducted on removing rain and haze from images, but none have studied removing rain and haze at simultaneously.  
On a real road, haze and rain tend to occur simultaneously. However, applying existing algorithms improves only part of the haze or rain. In this paper, the occlusion of haze and rain is both considered and propose a frequency-based haze and rain removal network.  
Overall, the framework of our work has three stages. The first is the frequency-based decomposition of the input image using the guided filter, and the second is the proposed FHRR-Net which extracts features for rain streaks and transmission maps to restore images. The network consist two symmetric encoder-decoder networks to train the low- and high-frequency networks separately to remove the rain streaks. Finally, the haze is removed with image degradation model.  
Proposed FHRR-Net are compared with two state-of-the-art methods on synthesized road test images and real urban road test images. Better results are shown in test data synthesized through experiments, as well as in real test images, than other state-of-the-art methods. Furthermore, object detection experiments validated that FHRR-Net is helpful for general real-world vision applications.  
Conceptualization, D.H.K. and M.T.L.; Data curation, W.J.A. and D.W.K.; Formal analysis, D.H.K., W.J.A., and M.T.L.; Methodology, D.H.K., W.J.A., M.T.L., and T.K.K.; Software, D.H.K., T.K.K., and D.W.K.; Validation, M.T.L. and T.K.K.; Writing--original draft, D.H.K. and M.T.L.; Writing--review & editing, M.T.L. and T.K.K. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Sciences and ICT (Grants No. NRF-2016R1D1A1B01016071 and No. NRF-2019R1A2C1089742).  
Not applicable.  
The Cityscapes data presented in this study are openly available in Cityscapes paper [32].  
The authors declare no conflict of interest.