# Rain Removal of Single Image Based on Directional Gradient Priors
## 1 Introduction
However, owing to the simple weighting of the high- and low-frequency components, the results of the high-frequency component are inaccurate, resulting in poor visual effect of the restored image. [PERSON] et al. [18] proposed a rain removal method based on a smoothing filter I0. In this method, the rain image and its corresponding low frequency are filtered by the smooth filter I0, and the result is compared with the original rain image by considering the minimum gray values as pixels of a rainless image. A rainless image recovered using this method is relatively clear, although some rain streaks are still retained. Because of the inherent overlap between the rain streaks and the background texture, most filter-based methods not only remove the rain streaks but also remove the texture details of the rainless area, resulting in an excessive smoothing effect in the restored background. Due to the powerful learning ability of deep convolution networks, deep learning has been used in many fields of computer vision, such as classification [19; 20; 21], pattern recognition [22; 23], and target detection [24; 25]. Similarly, deep learning has made great progress in the task of rain removal [26; 27; 28; 29]. [PERSON] et al. [26] proposed a deep detail network (DetailsNet) based on a deep convolutional neural network (CNN) to directly reduce the mapping range from a rainy image to a rainless image. [PERSON] et al. [27] proposed a new multi-stream dense connection CNN, which can automatically determine the rain density information and effectively remove the corresponding rain streaks under guidance of the estimated rain density label. [PERSON] et al. [28] also proposed a lightweight rain removal network (LPNet), which can obtain rainless images more quickly and significantly reduce the storage space required by the model. [PERSON] et al. [29] designed a lightweight deep convolutional neural network with the depth-guided non-local (DGNL) module to realize rain streaks and fog removal from the input rainy images. The rain removal methods based on deep learning have made significant progress and achieved good results. However, these methods require a large amount of sample data to drive the network training, and the sample data can be obtained only by using the degradation model to simulate the rain formation process. However, the imaging process of rain images of natural scenery is extremely complex. Most of the methods commonly used in the existing rain models cannot fully describe the internal mechanism of rain image degradation. Therefore, obtaining more real sample data is one of the greatest difficulties of a deep learning method. Similarly, the training of the network model and the adjustment of the model parameters also affect the network performance. To remove rain streaks from rain images and retain as much structural information of the original rain images as possible, we propose a single image rain removal method based on directional gradient priors. According to the directionality of the rain streaks and the sparsity of the rain layer gradient maps, two gradient sparse regularization terms are constructed to constrain the solution of the rain layer. To extract the structure of the rain streaks more accurately, a sparse coding method based on multi-scale dictionaries is proposed to encode the rain layer and realize a refinement of the rain layer solution. Because the parameters of the model are constrained by multiple constraint terms, the ADMM algorithm is used to solve the model alternately to obtain a rainless image with rich details. Our main contributions are as follows:  
* A rain removal method based on directional gradient priors is proposed, which can better optimize the rain layer and obtain a rainless layer (i.e., background layer) with richer texture. * By analyzing the structure of rain streaks, the horizontal gradient and vertical gradient prior constraints of rain layer are constructed to detect more accurate rain layer information.