## 3 Results and Discussion
### Image Restoration of Degraded Images
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**PSNR** & **Degraded Image** & **Standard cGAN** &
\begin{tabular}{c} **Hybrid Domain** \\ **Learning cGAN** \\ \end{tabular} \\ \hline Minimum & 18.072 & 18.602 & 20.715 \\ Maximum & 36.097 & 40.066 & 46.256 \\ Median & 27.112 & 34.603 & 37.786 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary statistics of PSNR values for degraded images and images reconstructed by the standard cGAN and by the hybrid domain learning cGAN on virtual degraded images. The highest value in each row is underlined. Figure 9: Image restoration result: (**a**) Visual comparison of pristine images (green), degraded images (red), images restored by the cGAN (yellow), and images restored by the hybrid domain learning cGAN (blue) in cases of validation using a virtual validation dataset. Quantified results of the image restoration quality based on (**b**) SSIM index and (**c**) PSNR index for the virtual validation dataset. As shown in Table 1, the hybrid domain learning cGAN consistently outperformed both the standard cGAN and the degraded images across all SSIM metrics. Notably, the median SSIM value for the hybrid domain learning cGAN (0.9813) closely approaches the maximum value of 1, indicating its strong capability to produce high-quality reconstructions with minimal variability. Similarly, Table 2 highlights the PSNR results, where the hybrid domain learning cGAN also achieves the highest scores across all statistics. The significant improvement in the minimum PSNR value (20.715 dB) compared to the standard cGAN (18.602 dB) reflects its robustness in handling even the most challenging degraded images. The maximum PSNR value (46.256 dB) further underscores the model's ability to produce near-pristine reconstructions under optimal conditions. Subsequently, we comprehensively evaluated the models' capabilities using actual degraded images obtained from the optical experiment. This evaluation aimed to verify the hybrid frequency-spatial domain-learning cGAN's ability to effectively restore actual degraded images. Figure 10 presents the image restoration results using 60 actual degraded images. The results for actual degraded images of the hybrid domain learning cGAN and the standard cGAN showed a trend similar to the results for the virtual degraded images. The hybrid domain learning cGAN achieved an average SSIM value of 0.9608, while the standard cGAN scored 0.9345. As illustrated in Figure 10c, the degraded images exhibited an average PSNR value of 26.383 dB. The standard cGAN improved this to 32.706 dB, while the hybrid domain learning cGAN further enhanced the results to 36.046 dB. This trend aligns with the SSIM findings, reaffirming the hybrid domain learning cGAN's superior performance in restoring actual degraded images compared to the standard cGAN. However, the SSIM and PSNR values for the reconstructed images from the actual degraded images were slightly lower than those from the virtual degraded images. This difference is attributed to additional factors, such as background noise, tilting, or aberration present in the actual acquired degraded images, which were not included in the virtual degraded image generation. Despite these challenges, the relative improvements compared to the degraded images indicate consistent quality enhancement, with the hybrid frequency-spatial domain learning cGAN demonstrating robust performance, even in actual degradation scenarios. Tables 3 and 4 provide detailed summary statistics, including the minimum, maximum, and median values of SSIM and PSNR, respectively. Table 3 reveals that the hybrid domain learning cGAN consistently produced higher SSIM values across all statistics compared to the standard cGAN and degraded images. The median SSIM for the hybrid model reached 0.9714, showcasing its ability to deliver high-quality restorations, even for real-world degraded images. This performance, combined with its higher minimum SSIM value (0.8702), underscores the hybrid model's robustness and reliability.