## 1 Introduction  
Shadows are a common phenomenon in nature when light is occluded by objects such as buildings, clouds, and trees. In the remote sensing image acquisition process, shadows also exist in images because of low sun elevation, off-nadir viewing angles, high-rise buildings, and uneven terrain. Shadows can be categorized as cast shadows and self-shadows. A cast shadow is the part of an object that is cast on the ground, while a self-shadow is the part that is not illuminated [1]. Cast shadows were the focus of the study presented in this paper. Although objects in cast shadow areas receive some scattered sunlight from the surrounding environment, their brightness is much darker than that of the surrounding non-shaded areas. As a result, information about other objects inside cast shadows is not adequately presented,which is detrimental to extracting and reusing the shaded information. In general, this influence is positively related to the cast shadow area. The area of an object shadow is related to the object size, height, and sunlight direction, and greater shadows usually cause greater radiometric information reduction. In an image, a cloud shadow is often much larger than the shadow of a ground object [2; 3]. In city construction, high-rise buildings always post larger shadows that occlude the adjacent roads and buildings. Moreover, with the development of spatial resolution of remote sensing images, this information reduction is more serious in image interpretation and affects image applications in other mapping and surveying processes. Thus, it is of great interest in the image reconstruction research arena to find a way to compensate for shaded information in remote sensing images to recover the lost information before beginning image processing steps. This compensated information can be further used in land cover classification [4], mapping, object recognition [5], etc. to improve the precision of the results. There are two types of shadow automatic compensation methods for remote sensing image image enhancement, compensation models. In the early 2000 s, image enhancement principles, which include Linear Correlation Correction (LCC) [6], Retinex [7; 8], and histogram matching [9], were applied to shadow removal for the purpose of improving the brightness and contrast of the shadow areas in images [10; 11; 12; 13; 14]. [PERSON] [15] utilized the invariant color property in the shadow area to detect shadow pixels and compensated for the shaded information loss based on histogram matching. [PERSON] et al. [16] proposed an approach for global shadow compensation that utilized fully constrained linear spectral unmixing. [PERSON] et al. [17] presented a machine-learning algorithm and an Enhanced Streaming Random Tree (ESRT) model for image segmentation and classification to extract shadow areas, after which color chromaticity and morphological processing were performed to remove shadows. [PERSON] et al. [18] designed a novel shadow detection and removal method based on leave-one-out optimization. First, they extracted the shadows and identified their neighboring lit regions. Next, they conducted histogram matching of the \(I\) component between the shadow regions, and the lit area was utilized to restore the shaded information. In summary, the compensation effect of their approach is related to the capability of the image enhancement algorithm and often relies on manual expertise to determine suitable parameter values. Nevertheless, it is challenging to achieve adaptive processing with this method, depending on the degree of shadow occlusion. Thereafter, a series of compensation models based on the Gamma correction method, color constancy principle, and other methods were proposed [19; 20; 21]. These methods combined information from shaded areas and non-shaded areas to establish suitable compensation models. [PERSON] et al. [22] took advantage of the Gamma correction principle to treat shadows as a multiplicative noise source.