## 4 Experiments
### Comparison with State-of-the-Art  
We exhibit and discuss the comparative experimental results and compare them with other schemes in this section [2; 3; 11; 12; 13; 39]. The comparison of watermarked image quality between our scheme and existing schemes, including PSNR, network architecture, watermark embedding domain and published time, is presented in Table 5.  
As Table 5 shows, in recent years, many screen-shooting watermarking methods have been presented [2; 3; 11; 12; 13; 39]. [PERSON] et al. [2] and [PERSON] et al. [39] were using traditional methods for resistance to screen-shooting attacks; they have good image quality, but the registration point is unstable and may not be able to extract the watermark. As deep learning develops, deep-learning-based watermarking algorithms have been widely studied in various network structures [3; 11; 12; 13], including U-Net, GAN, and CNN. For robust watermarking, HiDDeN [3] is, to our knowledge, the first end-to-end method using neural networks in the spatial domain, but it could not resist the screen-shooting attack. StegaStamp [11] was the first to propose a machine learning screen-shooting attack algorithm in the spatial domain. The algorithm has good robustness, but the image quality is slightly worse. ReDMark [3] was the first robust watermarking using deep learning in the frequency domain, and it has relatively good image quality; it also could not resist the screen-shooting attack. Table 5 displays that there have been few frequency-domain watermarking algorithms based on machine learning proposed in recent years, except ReDMark [3]. Watermarking algorithms in the frequency domain can help improve the imperceptibility of watermarking. Frequency-domain watermarking algorithms can guarantee enhanced imperceptibility and robustness of embedding after various attacks. Therefore, we investigate watermarking in the frequency domain via deep learning to improve the performance and efficiency in balancing the relationship between robustness and imperceptibility. However, the framework is limited by its unsuitability for color images. We also designed experiments to test the robustness of our networks and other existing schemes. The results are listed Table 6; (*) is the parameters used for each type of attack. The performance of the proposed method is illustrated by comparing with other deep-learning-based watermarking methods [3; 11; 12; 13], and the advantages of the proposed method are illustrated by experimental results. StegaStamp [11] proposed an end-to-end watermarking scheme for the print-camera process in the spatial domain. This method demonstrated very high robustness to print-camera distortions. Table 6 shows that StegaStamp has a good performance against perspective and light. However, the method has a poor performance against cropping and JPEG. The overall robust performance is considered to be positive in the spatial domain.The watermark information in ReDMark [3] is spread in a wide area of the image. ReDMark performs well against cropping, scaling, noise and visible watermarking. Compared with \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Methods** & **Network** & **PSNR** & **Published Time** & **Embedding Domain** \\ \hline StegaStamp [11] & U-Net & 29.88 & 2020 & Spatial domain \\ \hline HiDDeN [13] & GAN & 33.55 & 2018 & Spatial domain \\ \hline ReDMark [3] & CNN & 35.93 & 2019 & Frequency domain \\ \hline TSDL [12] & GAN & 33.50 & 2019 & Spatial domain \\ \hline [PERSON] et al. [2] & ISIFT and DCT & 42.30 & 2019 & Frequency domain \\ \hline [PERSON] et al. [39] & Geometric distortion & 39.10 & 2004 & Spatial domain \\ \hline The proposed (SSDeN) & CNN & 36.09 & 2022 & Frequency domain \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Methods comparison. the watermarking method based on the spatial domain, the watermarking method based on the transform domain is more robust. Although this method can resist traditional attacks robustly, it fails to resist screen-shooting attacks.