## 1 Introduction  
Due to the rapid development of internet technology and social media in recent years, many business models have gradually changed. Digital images have become one of the main media for information transmission. To protect the intellectual property rights and copyrights of the owners, digital watermarking is an indispensable technology. So-called \"digital watermarking\" refers to the hiding of secret information in digital media. Digital media can be images, videos, text, or audio, etc. The most common application is to embed trademarks in digital media to protect intellectual property. In 1994, [PERSON] et al. [1] proposed the term digital watermark and published a paper on undetectable digital watermark technology. Information hiding emphasizes the hiding of secret information in the carrier, making it difficult for human eyes to detect. In 1996, in the First International Workshop on Information Hiding [2], relevant terms for information-hiding technology were defined. In 1999, [PERSON] et al. [3] classified the structure of information-hiding technology. Information-hiding technology can be subdivided into steganography and watermarking. The goal of steganography is the same as cryptography, which is to protect secret information from being stolen by third parties. Watermarking is used in copyright protection, image authentication, medical, military, fingerprint, and other purposes. Steganography and watermarking are very similar in structure. They both hide secret information in digital media. However, the two technologies have different characteristics. Information-hiding technology has three basic attributes: capacity, security, and robustness [4]. The capacity indicates how much information a digital carrier can embed; security usually refers to its undetectability, and secret information will not be detected by statistical methods or steganalysis techniques; robustness indicates that the image can withstand various image-processing attacks, such as crop, scaling, rotation, noise, blur, compression, etc. In addition, for information-hiding technology, the ability to have imperceptibility is the top priority, and imperceptibility refers to the inability of human eyes to perceive secret information. Steganography focuses more on the imperceptibility, security, and capacity of secret information, while most watermarks prioritize their robustness. With the vigorous development and popularization of social media, huge amounts of image data are transmitted on the internet every day. According to Google's statistics in 2020, about 4.3 million GB of data are uploaded to Gmail, Google Drive, Google Photos, and other services every day. To meet the demand for storage space and maintain the efficiency of data transmission, image compression is a very important and indispensable technology. JPEG compression [5] is the most common image compression technology in the network transmission process, which can effectively reduce the capacity of digital images and maintain good image quality. However, this important technology, which is indispensable on the internet, is a big problem for digital watermarking. The basic standard technology of JPEG is based on discrete cosine transform (DCT) to compress images. The method involves converting the image into a DCT matrix and determining the coefficients through a pre-designed quantization table. Therefore, traditional solutions mostly use DCT conversion, adopting a DCT watermarking approach based purely on psychovisual thresholds to minimize distortion and enhance robustness. By contrast, our GAN-based approach uses deep learning to increase adaptability and resistance to attacks [6]. DCT is used to transform and segment the scrambled watermark into small portions to embed [7]. DCT ensures watermark insertion in the mid-band of co-efficient robustness [8]. Using DCT, LVT sub-bands are transformed to prepare them for watermark embedding with better perceptibility [9].