## 5 Conclusions  
Super resolution is a typical non-adaptive problem, and the space of all possible functions for mapping from a low-resolution image to a high-resolution image is large. This leads to a loss of detail and pseudo-detail in the super-resolution output. Increasing the number of supervisions in the super-resolution process can effectively reduce the ill-posedness. Therefore, a progressive super-resolution network based on multi-level supervision was proposed, and a lightweight BSRC with adjustable scale factor was designed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **PSNR (dB)** & **SSIM** \\ \hline \(\times 1\rightarrow\times 1.3\rightarrow\times 1.6\rightarrow\times 2 \rightarrow\times 4\) & 26.23 & 0.7928 \\ \(\times 1\rightarrow\times 2\rightarrow\times 2.3\rightarrow\times 2.6 \rightarrow\times 4\) & 26.59 & 0.7976 \\ \(\times 1\rightarrow\times 1.5\rightarrow\times 2\rightarrow\times 2.5 \rightarrow\times 4\) & 26.76 & 0.7986 \\ \(\times 1\rightarrow\times\sqrt{2}\rightarrow\times 2\rightarrow\times 2\sqrt{2} \rightarrow\times 4\) & 26.84 & 0.8079 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Ablation study for different scale factors of super-resolution components.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Loss Function** & **PSNR (dB)** & **SSIM** \\ \hline \(L_{1}\) Loss & 25.48 & 0.7821 \\ Perceptual Loss & 25.21 & 0.7908 \\ Perceptual Loss + \(L_{1}\) Loss & 26.39 & 0.7934 \\ Cross-level Loss & 26.84 & 0.8079 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Ablation study for different loss functions.  
The relationship between the number of BSRCs, the scale factor of each BSRC, and the performance of the multi-level supervision network was explored. Additionally, a cross-level loss function suitable for the multi-level supervision structure was designed. To fully test the performance of the super-resolution network, a dataset containing various types of ground regions was produced. Experiments were conducted on two publicly available datasets and the new dataset. The experimental results showed that the P2P-SR network outperformed existing SOTA methods. By further analyzing the experimental results, it was found that multi-level supervision has greater performance gains in super-resolution tasks with larger scale factors. It is speculated that the multi-level supervision network will have better performance in super-resolution tasks above four times. In future research, experiments will be conducted with multi-level supervision networks in super-resolution tasks at larger magnifications such as five times, eight times, and so on.  
Also, the relationship between multi-level supervision and the reduction in super-resolution ill-posedness will be further explored.  
Conceptualization, Q.X. and J.G.; data curation, M.L. and Q.Z.; methodology, Q.X. and M.L.; supervision, J.G. and Q.X.; validation, M.L.; writing--original draft, M.L.; writing--review and editing, M.L. and Q.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China under Grant 61972021.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to confidentiality.  
The authors declare no conflict of interest.