# STGAN: Swin Transformer-Based GAN to Achieve Remote Sensing Image Super-Resolution Reconstruction
## 4 Experiments
### Assessment of Indicators  
PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index) are standard evaluation metrics commonly used in the field of image super-resolution (SR) [53]. In order to evaluate the model performance more comprehensively, we also introduced metrics such as Perceptual Index (PI) [54], Learned Perceptual Image Patch Similarity (LPIPS) [55], Root Mean Square Error (RMSE), and Spectral Angle Mapping (SAM) [56], which are used to better measure the perceptual quality, reconstruction accuracy, and spectral consistency of an image. 1. PSNR measures the image quality by calculating the mean square error (MSE) between the original image and the processed image, and its value is measured in decibels (dB), which reflects the pixel-level difference of the image, and usually, a higher PSNR value indicates a better-quality image. The PSNR is calculated as: \[\text{MSE}=\frac{1}{N}\sum_{i=1}^{N}\left(I_{\text{original}}(i)-I_{\text{ reconstructed}}(i)\right)^{2}\] (13) \[\text{PSNR}=10\cdot\text{log}_{10}\bigg{(}\frac{(R^{2})}{MSE}\bigg{)}\] (14) where \(N\) is the total number of pixels in the image, \(I_{\text{original}}(i)\) and \(I_{\text{reconstructed}}(i)\) are the values of the original and reconstructed images at the ith pixel, respectively, \(R\) is the maximum possible pixel value (for 8-bit images, \(R\) = 255), and MSE is the mean square error. 2. SSIM further takes into account the brightness, contrast, and structural information of an image and evaluates the similarity of two images by comparing their differences in these aspects, with a value between 0 and 1, with the closer to 1 indicating the better quality of the image. The formula for calculating SSIM is: \[\text{SSIM}(x,y)=\frac{(2\mu_{x}\mu_{y}+C_{1})(2\sigma_{xy}+C_{2})}{(\mu_{x}^{ 2}+\mu_{y}^{2}+C_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+C_{2})}\] (15) \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Number of Image Pairs** & **HR Image Source** & **Ref Image Source** & **Location** & **Resolution of HR Images** & **Resolution of Ref Images** \\ \hline \multirow{4}{*}{Training set} & \multirow{4}{*}{4047} & WorldView-2, & \multirow{2}{*}{Google Earth, 2015 and 2019} & \multirow{2}{*}{Xiamen and 2019} & \multirow{2}{*}{0.5 m and 20.8 m} & \multirow{2}{*}{0.6 m} \\  & & & 2018 & & & \\ \hline \multirow{2}{*}{1 st test set} & \multirow{2}{*}{40} & WorldView-2, & \multirow{2}{*}{Google Earth, 2019} & \multirow{2}{*}{Xiamen, 2019} & \multirow{2}{*}{0.5 m} & \multirow{2}{*}{0.6 m} \\  & & & 2015 & & & \\ \hline \multirow{2}{*}{2 nd test set} & \multirow{2}{*}{40} & Microsoft & \multirow{2}{*}{Google Earth, 2019} & \multirow{2}{*}{Xiamen, 2019} & \multirow{2}{*}{0.5 m} & \multirow{2}{*}{0.6 m} \\  & & Virtual Earth, 2018 & & & & \\ \hline \multirow{2}{*}{3 rd test set} & \multirow{2}{*}{40} & GaoFen-2, & \multirow{2}{*}{Google Earth, 2019} & \multirow{2}{*}{Jinan, China} & \multirow{2}{*}{0.8 m} & \multirow{2}{*}{0.6 m} \\  & & 2018 & & & & \\ \hline \multirow{2}{*}{4 th test set} & \multirow{2}{*}{40} & Microsoft & \multirow{2}{*}{Google Earth, 2019} & \multirow{2}{*}{Jinan, China} & \multirow{2}{*}{0.5 m} & \multirow{2}{*}{0.6 m} \\  & & Virtual Earth, 2018 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information on RRSSRD public datasets. where \(\mu_{x}\) and \(\mu_{y}\) are the mean values of the images \(x\) and \(y\), \(\sigma_{x}^{2}\) and \(\sigma_{y}^{2}\) are their variances, \(\sigma_{xy}\) is their covariance, and C\({}_{1}\) and C\({}_{2}\) are small constants introduced to avoid a zero denominator. 3. PI and Natural Image Quality Evaluator (NIQE) [57] can be used as metrics for the evaluation of real images. NIQE and PI were originally introduced as nonreference image quality assessment methods based on low-level statistical features [58]. NIQE is obtained by computing 36 identical Natural Scene Statistical (NSS) features from the same-sized patches in an image. PI is calculated by merging the criteria of [PERSON] et al.