# Satellite Image Super-Resolution by 2D RRDB and Edge-Enhanced Generative Adversarial Network +
## 3 Materials and Methods
### Ablation Study  
To prove the feasibility of the proposed model, we conducted ablation experiments using different UDSN and EESN networks, different edge extraction methods, and adding other different loss functions. In all the ablation experiments, we used the pre-processed Kaggle data set and randomly selected 4000 images (72% training, 8% validation, and 20% testing) to conduct experiments.  
As shown in Table 4, we can see that the network architecture using RRDB with two-dimensional topology convolution has significantly improved the output results. By extensive ablation experiments, we discover that for the UDSN, using the 2D-topology RRDB has the best results, where the number of residual dense blocks (RDBs) in the RRDB is 3, while the number of convolutional layers in each RDB is 5 and they are all connected in 2D-topology. For the EESN, it still shows using the 2D topology convolutional layers in the RRDB brings the best SR performance. However, the number of RDBs in the RRDB becomes 2, and the number of convolutional layers in each RDB is 3. The final decided architecture for the generator is shown in Figure 2.  
Next, through experiments by using different edge extraction approaches, it is found that using Canny edge extraction (PSNR: 33.011 dB, SSIM: 0.918) method can bring better performance to the SR results than the Sobel (PSNR: 32.950 dB, SSIM: 0.906) and Laplacian (PSNR: 32.947 dB, SSIM: 0.913) methods. Finally, we sequentially add different loss functions to the original loss function. It is found that adding these losses into the model will yield a better performance for the final output SR image. The best performance happens when we add \(L_{\mathit{edge\_cst}}(\tau_{G})\), \(L_{\mathit{perc}}\), and \(L_{\mathit{edge\_perc}}\) into the original loss function.  
Therefore, the final loss function is decided from the ablation experiments in Table 4 and shown in Equation (8), where we combine \(L_{\mathit{img\_cst}}(\tau_{G})\) and \(L_{\mathit{edge\_cst}}(\tau_{G})\) into \(L_{\mathit{cst}}(\tau_{G})\), as in Equation (7). Based on the previous experiment experience, we set \(\alpha_{1}=0.1\), \(\alpha_{2}=0.009\).  
\[L_{\mathit{cst}}(\tau_{G})=L_{\mathit{img\_cst}}(\tau_{G})+L_{\mathit{edge\_ cst}}(\tau_{G}), \tag{7}\]  
\[L_{\mathit{final}}(\tau_{G},\tau_{D})=L_{\mathit{cont}}(\tau_{G})+0.001L_{ \mathit{adv}}(\tau_{G},\tau_{D})+5L_{\mathit{cst}}(\tau_{G})+\alpha_{1}L_{ \mathit{perc}}+\alpha_{2}L_{\mathit{edge\_perc}}. \tag{8}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**UDSN** & **EESN** &
\begin{tabular}{c} **Edge-** \\ **Extraction** \\ \end{tabular} & \(L_{\mathit{cont}}\) & \(L_{\mathit{adv}}\) & \(L_{\mathit{img\_cst}}\) & \(L_{\mathit{edge\_cst}}\) & \(L_{\mathit{perc}}\) & \(L_{\mathit{edge\_perc}}\) & **PSNR** & **SSIM** & **FSIM** \\ \hline DB & DB & Laplacian & & & & & & & & 31.843 & 0.874 & 0.988 \\ RDB & DB & Laplacian & & & & & & & & 31.401 & 0.845 & 0.985 \\
2D-RDB & DB & Laplacian & & & & & & & & 32.560 & 0.901 & 0.990 \\ RRDB & DB & Laplacian & & & & & & & & 32.074 & 0.882 & 0.985 \\
2D-RRDB & DB & Laplacian & & & & & & & & 32.774 & 0.899 & 0.991 \\
2D-RRDB & RDB & Laplacian & & & & & & & & & 32.755 & 0.903 & 0.990 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Ablation experiments.