## 3 Results
### Comparison of Model Parameters of Different Model Architectures and Various Evaluation Indicators  
The proposed method needs to store the secret key and the trained model parameters to generate watermarks, and how to reduce the amount of model parameters is very important. Therefore, we used depthwise separable convolution (DSC) [29] to ensure the feasibility of this idea. Compared with traditional convolution, depthwise separable convolution can reduce the number of parameters and calculations and has little effect on the model effect. To compare the effects of depthwise separable convolution on model training and results, we created two additional network models, DSC-1 and DSC-2. DSC-1 changes the convolutional neural network in the down-sampling part of the generator to the depthwise separable convolution, and the rest is the same as the original model; the generator part of DSC-2 is the same as that of DSC-1, and the convolutional neural network of the discriminator is changed to depthwise separable convolution and the rest is the same as the original model. The comparison between the original model and the other two models is shown in Table 6. The visualization results of the restored (retrieved) watermark of the three models are shown in Figure 10. \begin{table}
\begin{tabular}{c c c c c} \hline \hline Method & QF = 10 & QF = 50 & QF = 70 & QF = 90 \\ \hline ReDMark (MT-Net) [17] & - & 0.012 & 0.0 & 0.0 \\ \(\alpha\) = 1.0 & - & 0.035 & 0.004 & 0.0 \\ ReDMark (MT-Net) [17] & & & & \\ \(\alpha\) = 0.6 & - & 0.118 & 0.042 & 0.016 \\ ReDMark (JT-Net) [17] & & & & \\ \(\alpha\) = 1.0 & - & 0.013 & 0.002 & 0.001 \\ ReDMark (JT-Net) [17] & & & & \\ \(\alpha\) = 0.8 & - & 0.067 & 0.023 & 0.013 \\ ReDMark (JT-Net) [17] & & & & \\ \(\alpha\) = 0.6 & - & 0.173 & 0.107 & 0.079 \\ [PERSON] et al. [18] & 0.116 & (0, 0.005) & (0, 0.003) & - \\ Ours & 0.008 & 0.003 & 0.004 & 0.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison with other methods to the BER value of the restored watermark. In terms of generator parameters, the generator parameters are reduced by nearly half compared to the original model. The generator model size of the original model is about 1.27 MB, while DSC-1 and DSC-2 are reduced to 0.69 MB. In the image quality part of the restored (retrieved) watermark, DSC-1 and DSC-2 can still maintain good image quality for the restored (retrieved) watermark (the PSNR is 49.3 and 49.5 dB, respectively). However, the SSIM drops significantly after using DSC-1 and DSC-2, and it is already lower than 0.95. The human eyes can already see that the watermark restored (retrieved) by the model is different from the original watermark image. In the BER part, the BER of DSC-1 and DSC-2 has increased by about 0.01 but is still within an acceptable range. In addition, the depth of separable convolution will also affect the convergence speed of the model. The generator loss functions of the three models are shown in Figure 11, respectively. The original model (Figure 11a) has almost converged when Epoch is about 100, while DSC-1 (Figure 11b) only converges when Epoch is around 200, and DSC-2 (Figure 11c) converges when Epoch is around 300. The SSIM, BER, and convergence speed are slightly worse, but the benefit is that the number of parameters is greatly reduced, which is as much as half of the original model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & \
\begin{tabular}{c} **Generator** \\ **Parameters** \\ \end{tabular} &
\begin{tabular}{c} **Generator** \\ **Size (MB)** \\ \end{tabular} & **PSNR** & **SSIM** & **BER** \\ \hline Original & 331,715 & 1.27 & 49.348 & 0.959 & 0.006 \\ DSC-1 & 178,358 & 0.69 & 49.320 & 0.911 & 0.014 \\ DSC-2 & 178,358 & 0.69 & 48.497 & 0.900 & 0.016 \\ \hline \hline Model & \multicolumn{4}{c}{Restored watermark} \\ \hline Original & & & & \\ DSC 1 & & & & \\ DSC 2 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Various evaluation indicators for restored (retrieved) watermarks with different models.