## 1 Introduction  
Hyperspectral imaging is a sophisticated imaging technology [1] that collects information from hundreds of contiguous spectral bands across the spectrum, including ultraviolet, visible, and infrared light. Each pixel in hyperspectral images contains complete spectral information, essentially providing a unique spectral curve for materials present in the scene [2]. The ability of hyperspectral imaging to provide detailed spectral characteristics of different materials enables its wide application in fields such as environmental monitoring [3], agriculture [4], mineralogy [5], and surveillance [6]. Shadows in hyperspectral images significantly reduce the spectral intensity of materials and change their spectral characteristics [7]. The high spatial resolution of hyperspectral images leads to complex material compositions and a blurred shadow boundary [8]. To address these issues, current shadow processing methods generally include two stages: accurate shadow detection and effective shadow compensation. Hyperspectral shadow detection requires accurate identification of shadow areas. [PERSON] et al. [9] distinguished between shadowed and non-shadowed regions by analyzing the darkness in visible and near-infrared (NIR) spectra. [PERSON] et al. [10] used spectral data from NIR and short-wave infrared bands and used covariance matrices and matched filters for detection to distinguish shadowed from non-shadowed areas. This approach involves generating a shadow function and identifying core shadow regions through histogram thresholding. Yet, the limitation of these approaches often lies in the incorrect identification of environmental elements [11], such as the confusion between sunlit dark surfaces and shadows, or mistaking shadowed bright areas for sunlit ones. Furthermore, due to the gradual reduction of shadow components in the transition areas between shadowed and non-shadowed surfaces, it is not accurate to simply classify them as shadowed or non-shadowed. [PERSON] et al. [12] utilized the Inner-Outer Outline Profile Line (IOOPL) method, which extends analysis both inward and outward from shadow edges, aiding in the precise delineation of shadow boundaries, particularly in transitional areas. [PERSON] et al. [13] effectively handled the transition between shadowed and non-shadowed areas in high-resolution remote sensing images using a matting method. By minimizing the energy function that utilizes relationships between local pixels, this method provides the shadow probability for each pixel, ensuring smooth transitions at shadow edges. However, even if the shadow edges are meticulously processed pixel by pixel, existing methods still cannot handle transition areas well [14]. Hyperspectral shadow compensation is aimed at addressing the spectral attenuation and distortion caused by shadows to restore the spectral characteristics of material under well-lit conditions. [PERSON] et al. [15] utilized nonlinear unmixing to solve the nonlinear spectral shifts induced by shadows. They achieved this by extracting spectra from both shadowed and non-shadowed areas and using a nonlinear model to evaluate pixel abundance, then reconstructing pixels in shadowed regions. [PERSON] et al. [16] developed a network based on the CycleGAN (Cycle-Consistent Generative Adversarial Network), named SC-CycleGAN, eliminating the need for paired training data and shadow detection. The network, comprising two generators and two discriminators, learns to map between shadowed and non-shadowed domains, effectively compensating shadows while preserving the integrity of non-shadowed areas. Although these methods restore the spectra of materials, they overlook the spatial details of the surface. [PERSON] et al. [8] compensated for shadows by adjusting the spectral intensity of the image, thereby maintaining consistency in spatial and visual details before and after processing. However, a single adjustment parameter cannot solve the problem of nonlinear spectral attenuation caused by shadows.