# Frequency-Based Haze and Rain Removal Network (FHRR-Net) with Deep Convolutional Encoder-Decoder
## 1 Introduction  
Restoring degraded weather images to clean images is vital for many outdoor vision systems, including object detection [1, 2] and semantic segmentation [3, 4]. Most of these vision systems are designed based on good weather conditions and aim to work well under these conditions. However, in the real world, various weather conditions, such as rain and fog, degrade camera input images and the vision system. Under rainy and foggy conditions, rain streak occludes nearby objects, while fog produces hazy effects with light scattering, reducing the visibility of objects and the performance of vision systems. Figure 1 shows an example of applying an object detection algorithm to a hazy and rainy road image. In the rainy and foggy road image, object recognition error occurs. Figure 0(b) shows the result of the YOLOv3 algorithm [5]. The first row of Figure 0(b) shows incorrect recognition of a truck as a vase due to rain and fog. The second row of Figure 0(b) shows a low image recognition rate due to images degraded by the weather. Many camera-based advanced driver-assistance systems (e.g., pedestrian detection, lane departure warning, and traffic sign recognition) have been designed for driver convenience. As shown in the above example, rain and haze can cause errors in camera-based systems and cause serious accidents. Therefore, it is essential to study image restoration for road images degraded by rain and fog. However, road images have various characteristics, such as the presence of sky in the image and also a variety of road shapes, road materials, and backgrounds. Due to these characteristics, it is not easy to restore a degraded road image. Various methods have been proposed for restoring images degraded by rain and haze. Traditionally, the main focus was on restoration using hand-crafted features. More recently, researchers have mainly studied restoration using neural networks. Rain or haze removal-related studies can be classified as follows:  
Rain removal from a single image: Removing rain from a single image has been a challenging task because of the lack of information compared to video-based methods. In spite of such difficulties, many methods using hand-crafted features have been studied. For example, [PERSON] et al. [6] proposed a rain streak removal-based region detection algorithm that analyzes the rotation angle and the aspect ratio of the elliptical kernel at each pixel location, performing non-local mean filtering on detected rain streak regions. [PERSON] et al. [7] proposed a simple patch-based priors method using Gaussian mixture models. These priors can accommodate rain streaks at multiple orientations and scales. [PERSON] et al. [8] proposed a gradient domain method based on the observation that rain streaks influence X and Y gradients. However, rain removal using only hand-crafted techniques is not completely robust because the problem is ill posed. Recently, deep learning-based methods have been studied to solve this problem. For example, [PERSON] et al. [9] first proposed a deep learning-based rain streak removal method, DerainNet, and upgraded the model [10] by appling ResNet structure to reduce the mapping range, resulting in better convergence of loss functions. [PERSON] et al. [11] proposed a new rain streak image model and removed rain streaks effectively by adding a rain region layer. Haze removal from a single image: Removing haze from a single image is a difficult problem to solve because it is ill-posed in nature. Recently, however, learning-based methods have been studied, achieving significant progress [12; 13; 14; 15]. [PERSON] et al. [12] proposed a novel color attenuation method, creating a linear model for modeling scene depth. They trained the parameters of the model with a supervised learning method. [PERSON] et al. [13] introduced a CNN-based end-to-end system called Dehazenet. They also introduced a new nonlinear function, BRelu, to increase learning performance. [PERSON] et al.