## 2 Method
### Training Strategy and Loss Function  
We adopt the training strategy of StyleGAN-v2. This suggests that when training a network to generate high-quality images, the use of low-quality generated images can be beneficial to the training process, as illustrated in Figure 4a. In other words, we upsample the results from the lower scale and add them to the results from the next higher scale. The simplified representation can be expressed as Equation (6).  
\[images=\left(\alpha\times straight\right)+\left(\left(1-\alpha\right)*residual\right) \tag{6}\]  
_Images_ represents the generated images, _straight_ refers to the directly generated large-quality images, _residual_ refers to the upsampled low-quality images, and \(\alpha\) is the parameter that modulates the two levels of images. As training progresses, \(\alpha\) gradually increases to 1.  
Figure 3: Additional style structure: (**a**) is Generator; (**b**) is Style 2.  
To prevent the lower-level features from interfering with the generation of higher-level images, which could cause the well-decoupled weights in the \(w+\) space to become re-entangled, we retain the mixing regularization training strategy proposed in the StyleGAN series. The specific approach is as follows: during training, latent vectors (2) from different samples within the same batch are randomly mixed, and these mixed style vectors are injected into different layers of the generator. For example, the style vector of one sample can be applied to the earlier layers of the generator, while the style vector of another sample is applied to the later layers. This method enables the generator to learn the ability to handle different style information, thereby enhancing the disentanglement properties of the generative network and avoiding overfitting. The method is shown in Figure 4b.  
In Figure 4a, ToRGB refers to the convolutional layer that converts feature maps into three-channel color images, and Up represents an upsampling operation. In Figure 4b, a and b denote the style vectors of two different samples within the same batch. The loss function consists of the traditional loss of cGAN [34], as shown in Equation (7), the L1 loss is provided to control content information, as shown in Equation (8), and the AdIn loss is provided for injecting additional styles, as shown in Equation (9) [28].  
\[L_{cGAN}=E_{x,y}[logD(x,y)]+E_{x,z}[log(1-D)(x,G(x,z))] \tag{7}\]  
\[L_{L1}=\frac{1}{N}\sum_{i=1}^{N}|G(x,z)-y| \tag{8}\]  
\[L_{AdIN}=||f(g(x))-f(t)||_{2}+\lambda*\sum_{i=1}^{L}||\mu(f_{i}(g(x)))-\mu(f_{ i}(t))||_{2}+\sum_{i=1}^{L}||\sigma(f_{i}(g(x)))-\sigma(f_{i}(t))||_{2} \tag{9}\]  
\(X\) represents the input low-resolution images. y represents the ground truth corresponding to \(x\). \(z\) represents the random noise. \(G(x,z)\) represents the generated high-resolution images. \(N\) represents the number of samples in a batch.  
\(f\) represents the feature map of the corresponding convolutional layer, \(g\) represents the generator's computation process, \(t\) denotes the convolutional layer where additional an style needs to be injected, \(\lambda\) is the hyperparameter that adjusts the balance between content loss and style loss, \(i\) indicates the total number of convolutional layers where additional style is injected, \(\mu\) represents the calculation of the mean, and \(\sigma\) represents the calculation of the variance. The total loss is expressed in Equation (10).  
\[Loss=L_{cGAN}+L_{AdIN}+L_{L1} \tag{10}\]  
Figure 4: The training strategy, (**a**) Training structure of high-low scale addition (**b**) mixing regularization training structure.