## 1 Introduction  
Among the rich historical and cultural heritage of China, Tang Dynasty female terracotta figurines serve as important carriers of the social and artistic achievements of the Tang era. Their facial features are crucial for understanding the social landscape and aesthetic states of that time. However, due to natural erosion, human destruction, and other irresistible factors throughout history, many unearthed Tang Dynasty female terracotta figurines have suffered varying degrees of facial damage, such as the loss or damage of facial features. These damages not only affect the artistic expression of the artifacts, but also weaken their function as historical witnesses. Therefore, the precise image inpainting of these damaged Tang Dynasty female terracotta figurines is not only an urgent preservation task, but also an important means of protecting and inheriting Tang Dynasty cultural heritage. Currently, common inpainting techniques can be divided into physical inpainting and digital inpainting. Digital inpainting includes two-dimensional image inpainting and three-dimensional virtual inpainting. During physical inpainting, the detailed operations performed by experts may lead to the loss of original information, and may even cause further damage to the artifact itself. Three-dimensional virtual inpainting requires a vast amount of data and relies on the tight integration of multiple technical tools and processes. In contrast, image inpainting techniques exhibit significant advantages in terms of safety, accuracy, and convenience. As a result, in the field of cultural heritage inpainting, image inpainting techniques are gradually becoming the focus of research and application. Image inpainting is a technique that allows for filling missing areas with appropriate content [1], effectively restoring and protecting artifacts without compromising their physical integrity. Moreover, it enables an in-depth study and widespread dissemination of artifacts' original states in a virtual environment, achieving long-term preservation and educational outreach for cultural heritage. Image inpainting algorithms can be mainly divided into traditional algorithms, optical methods, and machine learning-based algorithms. Traditional algorithms [2; 3] are primarily classified into diffusion-based, exemplar-based, and sparse model-based methods. These approaches are suitable for completing images with similar structures in the surrounding background but have limitations when dealing with complex objects such as faces. Optical methods involve spectral imaging analysis, utilizing multispectral or hyperspectral data for cultural heritage image restoration. This technique captures spectral information across multiple bands, providing more details and information than traditional imaging, and has been widely applied in cultural heritage conservation [4; 5; 6]. However, spectral imaging generates large datasets, requiring significant computational resources for processing and storage. Machine learning-based image inpainting methods include support vector machines [7], nearest neighbor algorithms [8], clustering algorithms [9], Bayesian methods [10], random forests [10], generative adversarial networks (GANs) [11], and convolutional neural networks (CNNs) [12; 13]. Traditional machine learning algorithms are suitable for small-scale repairs with minor damage, but are less effective in handling complex image structures. The introduction of deep learning [14; 15], especially the application of GANs and CNNs, has brought revolutionary progress to the field of image inpainting. For instance, [PERSON] et al. proposed a multi-scale neural patch synthesis method based on the joint optimization of image content and texture constraints, significantly enhancing high-resolution image restoration performance [16]. Compared to the encoder-decoder structure based on CNNs, the GAN structure adds a discriminator, which more effectively learns the distribution of real samples [15].