## 2 Materials and Methods
### A Cascaded Spatial Frequency-Domain Generative Adversarial Network for SR: CSWGAN  
This paper proposed the CSWGAN, which was a cascade network of a self-attention-based GAN (SGAN) and wavelet-based GAN (WGAN), as shown in Figure 2.  
The main idea is to design a cascade framework to implement the application of spatial and frequency-domain features to obtain high-quality SR images.  
Figure 1: The self-attention mechanism for CSWGAN.  
The main architecture is based on SRGAN [26], with residual blocks serving as an important component in the network construction, enabling the recovery of photo-realistic textures on public benchmarks. The activation functions used in the generator and discriminator are different, with the generator employing PReLU to allow negative values to pass through the activation function. This helps to address the vanishing gradient problem and enhances the overall performance of the network by enabling the model to learn more complex data relationships. In the discriminator, LeakyReLU activation is used to prevent the need for max-pooling throughout the network.  
In order to enhance the learning of the spectral and geometric position information in remote sensing images, a self-attention branch is added outside the residual block of the backbone network. By incorporating self-attention mechanisms into feature extraction methods, dense global contextual information can be obtained, thereby establishing inter-dependencies between pixels. This enhances the network's utilization of global information and deep features. Then, the SR task is transformed into a wavelet coefficient prediction task, where the wavelet prediction module is tightly integrated with the wavelet reconstruction module within the GAN. By accurately predicting the corresponding wavelet coefficients, the LR image is decomposed into different scales and orientations, resulting in a high-quality HR image with rich texture details and global feature information.  
Figure 2: Network architecture of CSWGAN.  
The main task of the SGAN network is to learn and obtain the geometric structure information of the image, as well as low-frequency information such as the overall appearance and contours of the image. On the other hand, the WGAN is designed according to the characteristics of the frequency domain. Its main task is to learn high-frequency information such as image texture and edge. The SGAN learns spatial low-frequency features and their correlations through a self-attention mechanism. Based on the output characteristics of the SGAN, the WGAN can better distinguish noise and detail information, further optimize low-frequency and enhance high-frequency learning, thus improving the quality and fidelity. Therefore, by using the spatial-domain super-resolution (SDSR) output of the SGAN as the input to the WGAN and generating the final reconstruction output, the CSWGAN network can fully leverage the advantages of these two different networks. Moreover, training this cascade structure using multiple generators and discriminators is very time-consuming, so each adversarial system is trained separately first and then jointly in an end-to-end manner.