## 1 Introduction  
Techniques for imaging through turbid media have recently received considerable attention because of their potential applications such as atmosphere remote sensing, underwater photography, and even biomedical imaging [1; 2; 3]. The major difficulty encountered in these techniques is the loss of directionality of the incident light caused by multiple scattering among particles (water spray, dust, etc.), which leads to degradation of the image quality [4; 5; 6].  
Several studies that focused on polarimetric imaging techniques are of great interest [7; 8; 9]. By retaining and displaying polarization differences between airlight (natural illumination) and the direct transmission of light through an object in polarization images, polarimetric imaging can make it possible to enhance the visibility and contrast of images taken through turbid media. [PERSON], [PERSON], [PERSON], and collaborators [10; 11; 12; 13] mainly focused on image dehazing by employing linearly polarized information on light based on the fact that airlight is partially polarized light that can be detected. However, linear polarization (LP)-based methods rarely show satisfactory recovery results when it comes to rainy-day images. Two major reasons account for this phenomenon: one is the attenuation of thick clouds on rainy days, which causes a sharp reduction in the amount of light captured by cameras, but the circular polarization (CP) information in the scene remains stable based on the CP memory effect; the other is the characteristic of water spray, by which the interaction between airlight and water spray can turn natural light into circularly polarized light [14; 15; 16]. Moreover, since CP light is point-symmetric, it does not depend on the scattering angle, and can survive more multi-scattering events than linearly polarized light does [17]. The CP light maintains better polarization characteristics than LP for both forward and backward scattering, as shown in Figure 1a. The effects of size on the degree of polarization are shown in Figure 1b. The degree of polarization (DOP) is greater for LP than for CP for small sizes. When the size parameter is large, such as with a water drop, the DOP for CP is greater than for LP [18]. The circular polarization characteristics of light have been used in an effort to improve the image quality of underwater targets [19]. It provides another possible way to compensate for the deficiency of LP-based technologies in enhancing rainy-day image quality.  
In this study, we first analyzed limitations of traditional polarization image recovery methods based on linearly polarized light and then reported a CP imaging method combining the multi-scale analysis to image in rainy conditions and enhance visibility. Several scenes on a rainy day were captured using CP imaging devices. Then, the images were decomposed into various spatial frequency layers using wavelet transform. This operation concentrates the polarization information from objects and water spray to the low-spatial frequency components of the image; meanwhile, the specific structure information is concentrated to the high-spatial frequency components of the image. Furthermore, the degraded image could be recovered by employing the CP characteristics from the low-spatial frequency components. At the same time, the high-spatial frequency components were manipulated to reconstruct the details of the images by the nonlinear transform method. Experiments in rainy-day conditions were performed to demonstrate the effectiveness of the proposed method.