## 4 Experiment and Results
### Comparison with Other Methods  
To validate the effectiveness of the model, this study compares it with several existing FSR methods, including the traditional interpolation method Bicubic, as well as DIC [15], KDFSRNet [39], SISN [24], WIPA [17], and SPARNet [16]. Since SISN and KDFSRNet utilize the same CelebA training set as ours, we utilize the pre-trained weights for testing on our test set. For all other models, we train and test them using the official open-source code and the datasets used in this study. The results are subjected to both qualitative and quantitative analysis to provide a comprehensive evaluation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **ESEM** & **PA** & **FEM** & **PSNR** & **SSIM** \\ \hline
1 & & & & 27.389 & 0.817 \\
2 & & & \(\surd\) & 27.533 & 0.822 \\
3 & & \(\surd\) & & 27.425 & 0.819 \\
4 & \(\surd\) & & & 27.585 & 0.823 \\
5 & \(\surd\) & \(\surd\) & & 27.612 & 0.825 \\
6 & \(\surd\) & & \(\surd\) & 27.684 & 0.828 \\
7 & & \(\surd\) & \(\surd\) & 27.579 & 0.823 \\
8 & \(\surd\) & \(\surd\) & \(\surd\) & 27.744 & 0.830 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of ablation experiments on Helen. Table 2 lists the PSNR and SSIM values of our method and other compared methods tested on the datasets with the scale factor of \(\times\)8. Based on the experimental results presented in Table 2, it is evident that our model outperforms other methods in terms of achieving optimal PSNR and SSIM values on the CelebA, Helen, and LFW test sets. Specifically, the highest PSNR value of 27.744 dB is attained on the Helen test set, surpassing SPARNet [16], DIC [15], and KDFSRNet [39] by 0.343 dB, 0.954 dB, and 1.1229 dB, respectively. The corresponding SSIM value of 0.830 is also notably higher by 0.012, 0.033, and 0.042, respectively. On the LFW test set, our model achieves PSNR and SSIM values of 29.165 dB and 0.838, respectively, which are 0.687 dB and 0.336 dB better than [15,16], while exhibiting a higher SSIM value by 0.023 and 0.013, respectively. This is because SPARNet emphasizes spatial information while neglecting the interaction between feature channels, leading to a reduction in the quality of the SR images due to the underutilization of channel information. On the other hand, the DIC method lacks sufficient effective LR prior information, resulting in errors between the SR images and the HR images. KDFSRNet directly explores prior knowledge during the training phase, propagating from the teacher network to the student network, which introduces some dataset dependency. These experimental results highlight the superior performance of ours compared to the other methods in producing high-quality SR results. In order to gain a more intuitive understanding of the face reconstruction results, Figure 7 presents the SR results of the test set images using a scale factor of 8. Upon observation, it becomes apparent that while other compared methods also achieve satisfactory face reconstructions, our model produces results with a clearer face outline and more comprehensive facial structure. This improvement can be attributed to the preservation of crucial face structure information during the reconstruction process. In contrast, the face images obtained using the Bicubic interpolation method lack significant detail and appear excessively blurred due to a simplistic zooming approach. The DIC [15] method,