## 3 Experiments
### Ablation Studies  
To evaluate the effectiveness of different modules in the model, we conducted a series of ablation studies on the CelebA test sets for \(\times 8\) SR.  
_(1) Study on SCATM-T_: The SCATM-T, which consists of an SCAGB-T and a CMTB, aims to extract and promote both local facial details and global facial structures. It is the first attempt to explore the potential of inner feature maps in reconstructing plausible face images in the transformer-based FSR area. To verify the effectiveness of SCATM-T and its components, we designed three test models by removing different module parts. The test results are shown in Table 1.  
From the table, it can be observed that:  
1. The performance of SCATM-T without any components (i.e., removing SCATM-T) decreased dramatically. This is because the proposed model structure is much shallower without the SCATM-T, making it challenging to refine features. Moreover, without the processed fine-detailed feature maps from the SCATM-T, the Multi-scale Feature Fusion operation Module (MFFM) is greatly affected.
2. The quantitative metrics of SCATM-T with one single component inside are better than the no-component one above, demonstrating that both SCAGB-T and CMTB can enhance the representation ability of the model. However, SCATM-T with only SCAGB-T cannot guide anything, while SCATM-T with only CMTB cannot focus on feature map parts that are rich in features, limiting its performance.
3. Equipped with both of the carefully designed components SCAGB-T and CMTB, SCATM-T achieves the best performance in terms of all evaluation matrices, which proves that the combination of SCAGB-T and CMTB is complementary and can simultaneously promote both local facial details and global facial structures.  
_(2) Study on SCATM-B_: The SCATM-B, which contains an SCAGB-B and a CMTB, aims to enhance the low-level encoded features. Due to their comparable inner structures, we conducted similar experiments to the ones reported in the \"Study on SCATM-T\" part, the results of which are shown in Table 2. Similar observations and conclusions to those made in the previous section can be derived. However, it is worth noting that the performance of the model without SCATM-B is better than that without SCATM-T. This is because the SCATM-T and the MFFM are more complementary compared with the relationship between the SCATM-B and the MFFM; with one removed, the performance of others will also be greatly impacted.  
Moreover, we evaluated the influence on model performance of the number of SCATM-B, the results of which are shown in Table 3. From the table, it can be observed that the  
\begin{table}
\begin{tabular}{c c|c c c} \hline
**SCAGB-T** & **CMTB** & **PSNR\(\uparrow\)** & **SSIM\(\uparrow\)** & **LPIPS\(\downarrow\)** \\ \hline \(\times\) & \(\times\) & 27.30 & 0.7833 & 0.2047 \\ \(\times\) & ✓ & 27.55 & 0.7897 & 0.1831 \\ ✓ & \(\times\) & 27.54 & 0.7891 & 0.1839 \\ ✓ & ✓ & **27.63** & **0.7905** & **0.1797** \\ \hline \end{tabular}
\end{table}
Table 1: Ablation study of the components in the proposed SCATM-T. Please note that the **best** results are emphasized with **bold** in the experiment part for better visualization.  
model performs poorly without any SCATM-Bs, which proves that the SCATM-B plays a vital role in the model. Meanwhile, the performance of the model rises with the increase in the number of SCATM-Bs in a particular range. However, as the number of SCATM-Bs increases and exceeds four, the evaluation matrix change rate slows down and even decreases slightly. Additionally, the model size increases, which leads to an upsurge in the computational complexity of the model. Therefore, the number of SCATM-Bs is set to four for a good balance between model size and performance.