## 4 Experiment and Results
### Comparison with Other Methods
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{2}{c}{**CelebA**} & \multicolumn{2}{c}{**Helen**} & \multicolumn{2}{c}{**LFW**} \\ \cline{2-7}  & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** \\ \hline Bicubic & 23.572 & 0.637 & 24.138 & 0.681 & 24.893 & 0.693 \\ DIC [15] & 27.155 & 0.789 & 26.790 & 0.797 & 28.478 & 0.815 \\ KDFSRNet [39] & 27.245 & 0.793 & 26.515 & 0.788 & - & - \\ SISN [24] & 26.146 & 0.750 & 26.271 & 0.776 & 27.744 & 0.791 \\ WIPA [17] & 27.025 & 0.786 & 26.945 & 0.806 & 28.545 & 0.818 \\ SPARNet [16] & 27.167 & 0.789 & 27.401 & 0.818 & 28.829 & 0.825 \\ Ours & 27.449 & 0.800 & 27.744 & 0.830 & 29.165 & 0.838 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantitative comparison with other methods on CelebA, Helen and LFW for scale factor \(\times\)8. Figure 6: Curves of the training procedure. which incorporates face-prior knowledge to facilitate network learning, exhibits noticeable deformations in the eye position and blurred edges. The utilization of incorrect priors in LR face images leads to substantial errors in the reconstruction, which are further amplified by the multi-stage iterative process employed in it. Although WIPA [17], based on generative adversarial networks, demonstrates more realistic facial textures, it still exhibits artifacts that impair the visual effect and poorly recover essential eye positions. Figure 8 presents a comparison of local details for different methods. While KDFS-RNet [39] and SPARNet [16] excel in overall image reconstruction, they struggle to fully recover certain structural details, resulting in an overly smooth appearance. A specific example is the interdental region highlighted in Figure 8. On the other hand, SISN [24] incorporates attention separation between channels but fails to prioritize individual facial key parts, leading to a lack of clarity in the reconstructed face images. In contrast, our model exhibits richer facial textures (such as teeth, eyes, and hair) and well-defined edge contours, while minimizing distortion. These results demonstrate the effectiveness of our model in both face structure recovery and detail reconstruction. The aforementioned experiments were conducted on datasets that represent an unrestricted environment, which may differ significantly from real-world low-resolution face images. To bridge this gap, we applied the proposed method and CNN-based methods to real-world faces with unknown complex degradation, sourced from WiderFace [36] and WebFace [37]. In order to assess the naturalness of the recovered face images, we employed the NIQE since high-resolution reference images were not available. A lower value indicates a better reconstruction. The results of this evaluation are presented in Table 3, alongside comparisons with existing methods. Figure 8: Visual quality comparison of details with other methods. (**a**) Bicubic; (**b**) DIC; (**c**) KDFSRNet; (**d**) SISN; (**e**) WIPA; (**f**) SPARNet; (**g**) Ours; (**h**) HR. Figure 7: Visual quality comparison with other methods. (**a**) Bicubic; (**b**) DIC; (**c**) KDFSRNet; (**d**) SISN; (**e**) WIPA; (**f**) SPARNet; (**g**) Ours; (**h**) HR. Figure 9 presents a comparative analysis of the reconstruction results obtained by various methods on real-world datasets. It is evident that all methods experience degradation in performance when confronted with unknown complex degradation, resulting in smoothing and blurring of the reconstructed details. In contrast, our model demonstrates clear visual superiority and delivers more detailed facial reconstruction outcomes. It effectively captures and reproduces high-frequency textures and intricate details, thereby enhancing the recovery of key facial components.