# R-PreNet: Deraining Network Based on Image Background Prior
## 2 Related Works
### Model-Driven Methods  
Generally speaking, early filter-based methods and traditional prior based methods belong to the model-driven type. We will introduce representative works of these two aspects as follows. An image can be decomposed into low-frequency and high-frequency parts, with details and noise information predominantly located in the high-frequency part. Consequently, it is evident that raindrops in a rainy image are mainly distributed in its high-frequency portion. Thus, in the initial stages of rain removal from single images, guided filters [15] have been introduced as a universal tool for image prior representation, which decomposes the rainy image into its low-frequency part (LFP) and high-frequency part (HFP). Subsequently, [PERSON] et al. [16], [PERSON] et al. [17], [PERSON] et al. [18], and [PERSON] et al. [19] employed the characteristics of rain streaks and various guided filtering methods for single rain image deraining, achieving preliminary success. However, there are still issues such as leaving obvious rain streaks and missing background details, so there is room for further performance improvement in this method. Broadly speaking, rain-affected images are considered to be composed of a background layer and a rain layer:  
\[\text{O}=\text{B}+\text{S} \tag{1}\]  
where B denotes the background layer, which represents the target image to be obtained; S symbolizes the rain streak layer; and O represents the input image with rain traces. Thus, the problem of rain removal can be formulated as an image decomposition issue based on dictionary learning and sparse representation. Therefore, scholars no longer only rely on different guided filtering methods to remove rain from a single rain image, but have begun to study the physical properties of rain streaks themselves (such as sparsity and self-similarity), and introduced them into the deraining model as prior information, thus realizing the reconstruction of rainless images. [PERSON] et al. [20; 21] initially employed a bilateral filter to decompose the image into high-frequency and low-frequency components. Subsequently, the high-frequency component was further decomposed into \"rainy components\" and \"non-rainy components\" using dictionary learning and sparse coding. The rainy component was then removed from the image, preserving the majority of the original image details. This algorithm emphasizes training within the high-frequency layer rather than within the image domain, offering advantages in reduced computational resources and undisturbed low-frequency layer processing. However, this method is time-consuming, and, due to its heavy reliance on the bilateral filter preprocessing, the background is typically blurred, suggesting room for further performance optimization. In order to further obtain a clear background layer, a comprehensive exploration of the intrinsic properties of both the background and raindrops was conducted, and these properties were regularized to constrain the solution space. The classic methods include (1) The emergence of low rank due to the non-local similarity of raindrops [22]; (2) the Gaussian mixture model (GMM) employed for calculating the rain streak distribution across various scales and orientations [23; 24]; and (3) a sparse representation model based on some learning rain atoms [25]. Although these methods have modeled and referenced both rain streaks and background layers, they can only handle light rain streaks, making it difficult to handle heavy or sudden rain streaks, and there is still a problem of time-consuming processing. Research into these model-driven methods revealed that although incorporating physical prior information about rain patterns and background layers can help achieve rain image reconstruction, this prior information is usually subjective and incomplete, making it difficult to fully transfer existing prior knowledge in real rain images [13; 24; 26].