# Rain Removal of Single Image Based on Directional Gradient Priors
## 1 Introduction  
Images and videos captured on rainy days are easily blurred by the scattering of raindrops, which significantly limits the performance of outdoor visual processing systems, such as image segmentation, target recognition, and target tracking. Most previous studies have focused on video image rain removal [1; 2; 3; 4; 5; 6; 7; 8] by using prior information among the related frames [5; 7]. However, due to the need to obtain more information for detecting and removing rain streaks from adjacent frames, video image rain removal methods are unsuitable for single image rain removal. In recent years, single image rain removal has attracted more attention from academics, and its ideas can be roughly divided into three categories: sparse-coding- [9; 10; 11; 12; 13; 14; 15], filter- [16; 17; 18], and deep learning-based methods [19; 20; 21; 22]. The main idea of the sparse-coding-based rain removal method is firstly to decompose the rain image into low-frequency and high-frequency parts by reasonably describing the rain removal problem as an image decomposition problem; then, the accurate rain component is obtained from the high-frequency part by analyzing the internal structure of the image in the sparse domain; finally, the rain-free image is obtained by stripping the rain component from the rain image. As early as 2012, [PERSON] et al. [9] proposed a single image rain removal method based on sparse coding, which successfully removed the rain component from the rain image by performing dictionary learning and sparse coding. Similarly, [PERSON] et al. [10] decomposed the rain image into low-frequency and high-frequency parts by using the guided image filter, and then employed a hybrid feature set for dictionary learning and sparse coding to extract non-rain components from the high-frequency part. [PERSON] et al. [11] adopted a nonlinear rain model to remove rain streaksby constraining the correlation between the sparse coefficients of the rain components and rainless images. On the basis of image decomposition, [PERSON] et al. [12] further proposed an effective method using patch prior knowledge based on a Gaussian mixture model (GMM) to separate a rain layer and a rainless layer from a rain image. To better extract the information of rain streaks, [PERSON] et al. [14] proposed a sparse representation model based on analysis sparse representation (ASR) and composite sparse representation (CSR), which can more effectively utilize the global information of the image through a convolution operation. In 2017, [PERSON] et al. [15] proposed a hierarchical rain detection method that utilizes a rain detection matrix and a guided filter to separate the rain layer information from a rain image. When the prior information of the rain layer can be fully utilized, the rain removal methods based on sparse coding can detect the rain layer information better and remove the rain layers from rain images. However, due to the lack of prior information of the rain layer, most of the existing methods have problems, such as the loss of the original details of the image and the residue of rain streaks in the rain removal results, leading to the unnatural artifacts and fuzzy image edges in the restored image. The filter-based rain removal method removes the rain layer by filtering rain images according to the structural features of the rain signals. [PERSON] et al. [16] proposed a rain removal algorithm based on guided filtering (GF), which considers the rain patterns to have an almost equal influence on each pixel in the RGB color channels and filters the three channels to obtain the final rainless image. [PERSON] et al. [17] proposed a new method for removing the rain and snow by applying the low-frequency component of a single image, in which the low-frequency component containing a no-rain or no-snow component is used as a guide image to filter the high-frequency component. The filtered high-frequency component is combined with the low-frequency component to obtain the restored image.