## 4 Results
### Ablation Study
#### 4.3.2 Evaluate the Performance of WGAN in Frequency Domain  
Due to the limited use of frequency-domain-based super-resolution reconstruction networks, it was important to verify the detailed features of the WGAN-reconstructed images from the frequency-domain perspective.  
In this paper, three images with gradually increasing high-frequency information were selected for analysis, as shown in Figure 8. Because of the difficulty in recovering high-frequency information from remote sensing images, wavelet transformation was employed to extract the high-frequency information of different images, including the horizontal high frequency (cH), vertical high frequency (cV), and diagonal high frequency (cD) information. The SD and IE of the HR image and the results of each model are compared, as shown in Figure 9.  
It can be seen from Figure 9 that the distribution results of Bicubic, ESPCN, and ESRT are quite different from those of the HR images. The SD and IE distribution trends of SRCNN and SRGAN in different frequency bands were similar to those of the HR images, but the values were generally lower than those of the HR images. The SD and IE of the reconstructed feature map of the WGAN network were closer to the HR image feature map. It was proved that the WGAN can not only have a positive effect on the recovery of local high-frequency information, but also balance the information of different frequency bands to make it closer to the HR image.  
To further verify the performance of the WGAN, Table 6 shows the different evaluation standards of the other five models. Due to the introduction of the WGAN, the evaluation index of the overall image was no longer only from the spatial gray distribution and information content, but also from the spectrum and overall reconstruction error. Therefore, the SAM and RMSE were introduced.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Trained on Simulated Dataset**} & \multicolumn{3}{c}{**Trained on GF\_Sen Dataset**} \\  & **PSNR** & **SSIM** & **SAM** & **RMSE** & **PSNR** & **SSIM** & **SAM** & **RMSE** \\ \hline Bicubic & & & & 18.863 & 0.593 & 0.301 & 30.039 \\ SRCNN & 17.975 & 0.506 & 0.284 & 28.506 & 18.191 & 0.512 & 0.316 & 30.553 \\ ESPCN & 18.006 & 0.612 & 0.302 & 29.864 & 18.266 & 0.582 & 0.303 & 29.864 \\ ESRT & 19.092 & 0.461 & 0.219 & 25.322 & 20.287 & 0.669 & 0.191 & 24.484 \\ SRGAN & 18.654 & 0.611 & 0.385 & 36.675 & 19.217 & 0.639 & 0.372 & 36.168 \\ ESRGAN & 18.975 & 0.621 & 0.286 & 28.948 & 19.458 & 0.647 & 0.338 & 33.060 \\ WGAN & **22.142** & **0.836** & **0.178** & **18.217** & **23.564** & **0.855** & **0.188** & **17.421** \\ \hline \hline \end{tabular}
\end{table}
Table 6: Quality evaluation index results of different SR methods.  
Figure 8: Sample images used in frequency-domain feature statistics.  
The analysis of the results indicated that the WGAN achieved a higher PSNR and SSIM performance on the GF_Sen. In addition, comparing the SAM and RMSE, we can find that simple or lightweight networks may reduce spectral distortion and minimize errors to a certain extent because they had less complexity in the operation of the image. However, the RMSE and SAM values of the reconstruction results of the WGAN showed the smallest values, which especially proved the effectiveness of using the wavelet transform into the network to utilize the frequency-domain features.