## 2 Historical Background
### Image Inpainting of Cultural Heritage  
Image inpainting is a technique that allows for filling in missing areas with appropriate content, aiming to predict the missing regions from a single damaged image [1], i.e., two-dimensional image inpainting. It has many applications in image editing, such as occlusion removal and the inpainting of old photographs. In the current research field, image inpainting work for cultural heritage mainly focuses on murals, ancient paintings, and other types of cultural heritage with relatively clear and abundant data [4; 13; 19; 20; 21]. Image inpainting algorithms can be divided into three categories: traditional algorithms, optical methods, and machine learning-based image inpainting algorithms. Additionally, these three methods can be combined to leverage their respective advantages, achieving more efficient image inpainting results. Traditional algorithms mainly rely on data similarity, with their core being texture generation or patch-matching techniques. They are based on the assumption that the missing parts should be restored by selecting similar textures or patches from known regions. Traditional algorithms can be simply divided into  
Figure 1: **(a)** Painted terracotta female figurine; **(b)** standing terracotta female figurine; **(c)** seated terracotta female figurine with a tricolor phoenix crown and bird (Source: the Palace Museum). Figure 2: Tang Dynasty male-dressed female terracotta figurine (Source: Shaanxi History Museum). three categories: diffusion-based methods [35], exemplar-based methods [36], and sparse model-based methods [37] for image inpainting [3,4]. Regarding diffusion-based methods, ref. [38] proposed a diffusion probability model that reconstructs high-definition images of traditional Chinese landscape paintings through an iterative denoising process. Regarding exemplar-based methods, Ref. [2] proposed a classic inpainting method that removes a large object based on the calculation of patch priority and similarity while preserving important texture and structural information. Many papers have improved the Criminisi algorithm to achieve image inpainting for cultural heritage [17]. [PERSON]. [39] used an improved Criminisi algorithm based on structure tensors to restore damaged images of ancient fabrics, showing that the algorithm results in more reasonable texture structures and fewer inpainting traces. [PERSON]. [40] proposed a structure-guided virtual inpainting method based on the Criminisi algorithm, reconstructing missing structural lines of silk artifacts through adaptive curve fitting and optimizing the inpainting priority and sample block size selection mechanism to improve the inpainting effect. Regarding sparse model-based methods, [PERSON]. [41] proposed a line-drawing-guided mural inpainting method that addresses the digital restoration of Dunhuang murals by sparsely modeling texture similarity and structure continuity. Traditional algorithms perform well in background inpainting tasks and are widely deployed in practical applications. However, because they assume that the missing patches can be found somewhere in the background area, if there is not enough similar structural information near the missing area or if the image itself is complex and irregular (such as faces or objects), structure-guided virtual inpainting methods may face challenges, as they rely on known information to infer and reconstruct the missing parts [42]. Spectral imaging technology also plays an important role in the field of cultural heritage image restoration [4, 5, 6]. This technology combines image capture and the analysis of an object's spectral reflectance, allowing for the characterization of the object's features across multiple bands. Spectral imaging analysis includes multispectral imaging, hyperspectral imaging, and Fourier transform spectral imaging. [PERSON].