## 1 Introduction
### Related Works
#### 1.1.2 Watermarking Technology Based on Deep Learning  
In 2023, [PERSON] et al. (2025) proposed a new blind digital watermarking method for color images: a downsized color image embedded into a host color image. The watermarking procedure is performed by dividing the host image into blocks of eight pixels non-overlappingly, performing discrete cosine transform (DCT) for each block of each channel, and manipulating the magnitudes of three designated DCT coefficients using the appropriate minimization constraint. Experimental results have shown that the watermarked image produced by this watermarking method outperformed four other methods based on zero-normalized cross-correlation (ZNCC), a metric that measures the similarity between the original and retrieved watermarks, with values closer to one indicating higher accuracy. Furthermore, watermarks were still at a fair level of imperceptibility, as proved by the various measures of peak signal-to-noise ratio and mean structural similarity. This has accompanied the new paradigm in color image watermarking--the adoption of deep residual networks in the denoising and resolution enhancement of retrieved watermarks. Overall, more than 0.88 ZNCC levels are achieved by the residual network in super-resolving the watermark images by a factor of sixteen. [PERSON] et al. [17] proposed a watermarking method (ReDMark) based on a convolutional neural network. After training, the network can provide a blind watermark for grayscale images. The method includes three modules: Embedding, Attack Layer, and Extraction. The structure of Embedding and Extraction is fully convolutional networks (FCN), and the Attack Layer simulates various image-processing attacks to improve the model's robustness. In addition, the method also introduces a strength factor to control the balance between imperceptibility and robustness. According to the experimental results, the method has good imperceptibility and robustness, but in the case of \(\sigma=25\) Gaussian blur, where \(\sigma\) represents the standard deviation, with higher values indicating stronger blurring effects, 10% salt-and-pepper noise, and 20% cropping, the robustness is poor.  
In 2020, [PERSON] et al. [18] introduced a watermarking method designed to achieve both robustness and blindness. This approach leverages the fitting capabilities of deep neural networks to learn and encapsulate the watermarking algorithm, training the network in an unsupervised manner. The architecture features a one-way deep neural network comprising five key modules: Encoder, Embedder, Invariance, Extractor, and Decoder. Among them, Invariance is the key factor for the robustness of the method, and the fully connected layer is used to map the feature to another space to improve the tolerance for errors. According to the experimental results, this method has good imperceptibility and good robustness for most image-processing attacks. It is only inferior in certain severe distortion situations, such as 65% cropping, a compression ratio of quality factor 10, and 90% salt-and-pepper noise.  
The comparative analysis of prior methods and proposed work is shown in Table 1.  
\begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Key Features** & **Limitations** & **How Our Work Addresses** \\  & & & **These Limitations** \\ \hline [PERSON] et al. (2024) [20] & RIV-GAN framework; uses convolutional layers and residual blocks for encoding. GAN-based robust watermarking; uses a high-pass filter and weighted loss. Original GAN architecture; unsupervised learning with generator and discriminator. Conditional GAN; uses additional information for control. DCGANs with GAN architecture for training. DCGANs with GAN architecture for training.