## 5 Experimental Results and Discussion
### Objective Evaluation of the Proposed Watermarking Model  
Objective evaluation employs quantifiable metrics, such as PSNR, SSIM and analysis of watermarking robustness, to rigorously assess the performance of watermarking models. These metrics offer a standardized approach for evaluating image quality and structural preservation, thereby ensuring consistent and reproducible measurements. Utilizing these measures allows for a precise assessment of the impact of watermarking on image fidelity and facilitates comparisons between different methods. Table 1 presents the PSNR and SSIM values for the watermarking models, which are calculated by averaging the results from 5000 encoded images in the CCTSDB dataset. Five existing state-of-the-art (SOTA) watermarking models are used for comparison: HiDDeN [8], ReDMark [7], DA [46], TSDL [47], and MBRS [48]. We attempted to replicate the experiments conducted by DA and TSDL, but we were unable to fully reproduce their performance. Therefore, we use the published results from their respective articles for comparison. Additionally, MBRS provides a pre-trained model, and we use their test results for evaluation. To ensure a fair comparison, the binary watermark length is set to \(L=30\) for all the models under consideration. As shown in Table 1, our FIAE-GAN model outperforms the other five SOTA watermarking models regarding SSIM. Specifically, FIAE-GAN achieves a PSNR of 35.89, 3.75 dB higher than HiDDeN's PSNR of 32.14 and 2.19 dB higher than DA's PSNR of 33.70. Compared to MBRS, which has a PSNR of 35.08, FIAE-GAN demonstrates an improvement  
Figure 10: Subjective evaluation through SIFT feature matching between the original and watermarked images. Figure 9: Subjective evaluation through histogram comparison of the original and watermarked images. of 0.81 dB. Regarding SSIM, FIAE-GAN achieves a value of 0.9679, surpassing HiDDeN's SSIM of 0.9315 by 0.0364. Compared to MBRS, which has an SSIM of 0.8914, FIAE-GAN's SSIM is 0.0765 higher, indicating that FIAE-GAN better preserves image details and overall visual quality. In addition, both ReDMark and FIAE-GAN methods perform almost equally well in terms of image quality retention after watermarking, with ReDMark having a marginally better PSNR. However, FIAE-GAN outperforms RedMark in terms of SSIM, suggesting that our method better preserves the structural similarity of the original image after watermarking. To evaluate the robustness of the proposed watermarking model, the bit accuracy (BA) is calculated by averaging the results across all tested images. The BA computed based on \(W_{out}\), as defined in Equation (7). We optimize the loss function presented in Equation (8); a lower loss value \(L_{\mathrm{D}}\) corresponds to higher BA results. The BA results are presented in Figure 11, where a comparative analysis of the proposed method is conducted against HiDDeN [8], TSDL [47], MBRS [48] and ReDMark [7] under various types of noise attacks. The average BA values of HiDDeN, TSDL, MBRS, ReDMark, and our FIAE-GAN are 0.7969, 0.7984, 0.9551, 0.8534, and 0.9794, respectively, which demonstrates that our FIAE-GAN significantly outperforms the other four models. Specifically, compared to HiDDeN, FIAE-GAN demonstrates a 22.9% improvement, while against TSDL, the improvement is of approximately 22.6%. In comparison to ReDMark, FIAE-GAN shows a 14.8% increase in performance. Even though MBRS achieves a BA of 0.9551, FIAE-GAN still surpasses it by 2.5%, making it the most robust model among all tested. It is noteworthy that, concerning JPEG compression and Gaussian noise, our FIAE-GAN demonstrates superior robustness compared to HiDDeN, TSDL, and ReDMark. For a watermarking system to be practical, it must be robust to a broad spectrum of image noises, extending beyond those encountered during training.