## 2 Method
### Network Structure
The super layer of the generator (G-super) generates images with higher quality (such as 512 \(\times\) 512 or 1024 \(\times\) 1024). During this process, the network layers no longer receive style information from the low-resolution image. Instead, the required style control is solely obtained from Style 1 and Style 2. The structure design of the generator and Style 1 is shown in Figure 2.  
In Figure 2, the latent vector z is mapped to the style space \(w+\) through the mapping network. The multilayer perceptron (MLP) transforms the style vector into scaling weights. A that can be used by the convolutional layers. It should be noted that the style vector in \(w+\) is intended to directly affect the feature maps. However, StyleGAN-v2 proposes that converting the style vector into scaling weights that influence the convolutional layer weights can achieve the same effect while being more computationally efficient. In Figure 2, \(w\) is the convolutional layer weights and \(b\) is the bias. StyleGAN-v2 designs Mod and DeMod to inject style information into the generator. Mod is used to inject style and scale the convolutional layer weights, as shown in Equation (1), while DeMod is used to normalize the convolutional layer weights, making style control more flexible and efficient, as shown in Equation (2). \[w^{\prime}_{i,j,k}=S_{i}*w_{i,j,k} \tag{1}\]  
Figure 2: Network structure of generator: (**a**) is the generator of styleGAN-V2, and (**b**) is the generator of DSpix2 pix in Figure 1.  
\[w^{*}_{i,j,k}=\frac{w^{\prime}_{i,j,k}}{\sqrt{\sum_{i,k}w^{\prime 2}_{i,j,k}+ \epsilon}} \tag{2}\]  
\(S\) represents the scaling weights of each channel mapped from the \(w\)+ space, \(w_{i,j,k}\) represents the original weights, \(w^{\prime}_{i,j,k}\) represents the modulated weights, \(w^{\prime}_{i,j,k}\) represents the normalized weights of the convolutional layers, \(i\) is the channels of the input feature maps, \(j\) represents the channels of the output feature maps, and \(k\) represents the size of the convolution kernel. \(\epsilon\) represents a very small constant to prevent the denominator from being zero. Although this is not entirely identical to directly scaling the feature map, experiments of StyleGAN-v2 have shown that it does not significantly affect the quality of the generated images. Since the design of StyleGAN-v2 is to generate images with the same style but random content, its input is typically a random constant of size 4 \(\times\) 4 \(\times\) 512. To leverage this characteristic for generating super-resolution images, we need to replace the random constant with a certain vector with content information extracted from the low-resolution image. Therefore, we add the G-Encoder. This means we use convolutional layers to encode low-resolution images into a 4 \(\times\) 4 \(\times\) 512 constant, which are then fed into the decoder of the generator to provide content information, thereby generating high-resolution images. In the encoder, the design of the style block is similar to that of the decoder, with the only difference being that the upsampling operation is replaced by downsampling to accommodate the low-resolution image input. Although the style information of the image is typically well preserved during the encoding process, we still extract the style features of the remote sensing data from the style space \(w\)+ to ensure the stability of the image encoding. At the same time, we retain the input of random noise B to allow the network to generate more details, improving the realism and quality of the image. And we have added skip connections similar to those in U-Net between corresponding layers of the encoder and decoder to continuously provide style and content information from the low-resolution image. In the experiment, it was found that using the generator in Figure 2b can stably produce high-resolution remote sensing images with the same content information as the low-resolution images, especially at lower scales.