# A Shearlets-Based Method for Rain Removal from Single Images
## 1 Introduction  
Rain removal from a single image is an important issue in processing outdoor vision problems. In fact, the outdoor images are often degraded by the rain streak and other bad weather conditions, and these bad weather conditions can lead to the change of local or global intensities and color contrast in real images, thus causing unclear visible scenes. Such degradation severely affects the performance of algorithms in computer vision systems. Therefore, the removal of rain streaks is essential. In recent years, the rain removal problem has caused more and more attention. There are many approaches for rain removal using different modelings. They can be classified into two kinds, including the video-based methods and the single image-based methods. In fact, there are many literatures for the video-based methods [1; 2; 3; 4; 5; 6; 7; 8; 9; 10], the main idea is taking advantage of the rich detail of multiple relative images and the similarity of the image sequences to detect rain streaks and recover the background layer. For instance, [PERSON] and [PERSON] [1] proposed a correlation model to capture the dynamics of rain in video, then removed rain streaks by a physics-based motion blur model. That is, once rain streaks are detected, the corresponding pixel value of rain is obtained by averaging the rain-free temporal neighbors. In [4], [PERSON] and [PERSON] found that the video rain visibility relies heavily on the exposure time and the depth of field, based on this fact, they introduced a self-adaption parameter model to remove rain streaks efficiently. In addition, [PERSON] in [2] gives a new rain removal model, which is based on two priors, one is rain streaks that are almost the same in RGB channels and the other is rain streaks that do not appear everywhere in video. Recently, [PERSON] et al. proposed a novel tensor-basedvideo rain streaks removal approach via utilizing discriminatively intrinsic priors in [10], by fully considering the discriminatively intrinsic characteristics of rain streaks and clean videos, which needs neither rain detection nor time-consuming dictionary learning stage. This method is based on the following priors, including that rain streaks are sparse and smooth in the rain-drop direction and the clean video is smooth along the rain-perpendicular direction, which are both global and local correlation in time direction. For the single images-based methods, it is more difficult than video-based method due to the limited single image information, thus there are fewer works for single image rain removal. The most successful methods are given in literatures [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. For instance, in [11], based on the assumption that a rainy image can be represented by the rain layer and the background layer, the author proposed a dictionary learning method-based nonlinear screen blend model for rain removal from single images. The key for this method is that by sparse coding of two layers using the sparse dictionary, by learning sparse dictionary, the accurate layer decompositions are obtained. Moreover, in [14], [PERSON] et al. decomposed the rainy image into low frequency and high frequency parts, and applied an MCA-based dictionary learning model to split the rain streaks layer in the high frequency domain. Following this idea, the author in [16] introduced the structure information into consideration, but the estimated background layer tends to be blurry. Then [PERSON] et al. gives another additional model in [13], which is a linear super-imposition of the desired background layer and the rain streak layer, which is an energy minimization model, and the Gaussian mixture model is utilized to learn the corresponding patch-based priors for two layers. The advantage of this model is that it can detect different orientations and scales of the rain streak, which leads to state-of-the-art rain removal results.