## 4 Experiments
### Ablation Studies
In this part, we create three different multi-scale feature fusion models to demonstrate the effectiveness of the MFFM, whose results are shown in Table 4.  
It can observed from the table that: (a) The experiment demonstrates the importance of incorporating multi-scale features in the image reconstruction process since the model without multi-scale feature fusion performs the worst. (b) Using an addition or concatenation layer to fuse multi-scale features has proven beneficial. However, it is imperative to note that these techniques are inadequate for the complex multi-scale feature fusion process. (c) The model with the carefully designed MFFM achieves the best performance regarding PSNR, SSIM, and LPIPS. This proves that a suitable feature fusion strategy like MFFM can benefit the image reconstruction process. _(4) Study on PRUM/PRDM_: The PRUM/PRDM aims to establish direct relationships among adjacent pixels for better face structure preservation and further strengthen the overall image reconstruction performance. It is the first attempt to establish direct relationships among adjacent pixels in reconstructing highly structured face images in the transformer-based FSR area. In this part, we compare its performance with the usual deconvolution layers, of which results are shown in Table 5. \begin{table}
\begin{tabular}{c|c c c} \hline \hline
**Approaches** & **PSNR\(\uparrow\)** & **SSIM\(\uparrow\)** & **LPIPS\(\downarrow\)** \\ \hline Not Applied & _27.67_ & 0.7917 & 0.1846 \\ Only Add & _27.72_ & 0.7926 & 0.1809 \\ Only Concat & _27.73_ & 0.7930 & 0.1800 \\ Our MFFM & _27.77_ & **0.7941** & **0.1766** \\ \hline \hline \end{tabular}  
* The **best** results are emphasized with **bold**. \(\uparrow\) and \(\downarrow\) indicate whether higher or lower evaluation matrix values correspond to better image quality, respectively.  
\end{table} 
Table 4: Performance comparisons of different approaches of the multi-scale feature fusion process. \begin{table}
\begin{tabular}{c c|c c} \hline \hline
**AGB-B** & **CMTB** & **PSNR\(\uparrow\)** & **SSIM\(\uparrow\)** & **LPIPS\(\downarrow\)** \\ \hline \(\times\) & \(\times\) & 27.63 & 0.7911 & 0.1896 \\ \(\times\) & ✓ & 27.73 & 0.7935 & 0.1788 \\ ✓ & \(\times\) & 27.74 & 0.7938 & 0.1779 \\ ✓ & ✓ & **27.77** & **0.7941** & **0.1766** \\ \hline \hline \end{tabular}  
* The symbols \(\surd\) and \(\times\) indicate whether or not a corresponding block is included, respectively. The **best** results are emphasized with **bold**. \(\uparrow\) and \(\downarrow\) indicate whether higher or lower evaluation matrix values correspond to better image quality, respectively.  
\end{table} 
Table 2: Ablation study of the components in the proposed AGTM-B. \begin{table}
\begin{tabular}{c|c c c} \hline \hline
**AGTM-B Numbers** & **PSNR\(\uparrow\)** & **SSIM\(\uparrow\)** & **LPIPS\(\downarrow\)** \\ \hline
**0** & _27.63_ & _0.7911_ & _0.1896_ \\
**2** & _27.71_ & _0.7933_ & _0.1797_ \\
**4** & _27.77_ & _0.7941_ & _0.1766_ \\
**6** & _27.76_ & _0.7938_ & _0.1775_ \\ \hline \hline \end{tabular}  
* The **best** results are emphasized with **bold**. \(\uparrow\) and \(\downarrow\) indicate whether higher or lower evaluation matrix values correspond to better image quality, respectively.  
\end{table} 
Table 3: Performance comparisons of different AGTM-B numbers in the proposed method. It can be observed that the pixel deconvolutional and pixel shuffle layers can obtain barely satisfactory reconstruction results. This is because the inner feature maps produced by these layers have no direct pixel relationship. At the same time, our proposed PRUM/PRDM achieves better reconstruction results due to its ability to preserve face structure based on relative pixel positions.