## 3 The Proposed Network Model
### Discriminator Structure  
The structure of the discriminator is shown in Figure 9. The discriminator is the same as that in the SRGAN. The discriminator contains eight convolutional blocks together as a structure, as shown in the figure. The infrastructure in each module is also shown. To avoid the problem of neuron death, Leaky ReLU is selected as the activation function of the network. The convolution core of each convolution layer in the network is set to \(3\times 3\), followed by a number of channels increasing from 64 to 512 and a doubled rate compared to the original. At the end of the network, two full connection layers and one sigmoid activation function are introduced to obtain the probability of sample data classification. Mathematically, a discriminator network is considered to composed of the following form of a residual network:  
\[f(x,\theta)=F(x,\{W_{i}\})+x, \tag{7}\]  
where \(x\) is the input value, \(\theta=\{W_{1},W_{2},\ldots,W_{i}\}\) is the parameter set, and \(F(x,\{W_{i}\})\) is the residual network to be trained. For example, if \(F\) represents \(W_{i}h(W_{i-1}x)\) and \(h\) represents the activation function, then the final input of the discriminator ignoring bias can be represented as \(D(x,\theta)=H(f(x,\theta))\), where \(H\) refers to the distance metric difference.  
The loss function exists in the form of fusion loss. In addition to the pixel-by-pixel loss defined by \(L_{1}\) loss, it includes perceptual loss and adversarial loss. The final fusion loss is obtained by balancing and accumulating the weight coefficients of different losses. The pixel loss function is shown in Equation (8).  
\[L_{1}=\frac{1}{WHC}\sum_{i}^{W}\sum_{j}^{H}\sum_{k}^{C}\|l_{i,j,k}^{h}-l_{i,j, k}^{g}\|, \tag{8}\]  
where \(H\) and \(W\) represent the size of the matrix, and \(C\) represents the number of channels. In addition to pixel loss, the loss in this paper refers to the perception loss concept proposed in the SRGAN. As previously mentioned, SRGAN uses the pretrained VGG network to extract both the G network super-resolution reconstruction results and the high-definition image features. This can be defined as the Euclidean distance between the extracted features, as shown in Equation (9).  
\[L_{\text{VGG}/i,j}^{SR} =\frac{1}{H_{i,j}W_{i,j}}\sum_{x=1}^{H_{i,j}}\sum_{y=1}^{W_{i,j}} \left(\phi_{i,j}(I^{HR})_{x,y}-\phi_{i,j}(G_{\theta_{G}}(I^{LR}))_{x,y}\right) ^{2}, \tag{9}\]  
where \(G_{\theta_{G}}(I^{LR})\) represents the super-resolution reconstruction image of the generator subnetwork. As mentioned above, \(H_{i,j}\) and \(W_{i,j}\) represent the dimension values of the feature map in the feature extraction network, inside the VGG feature extraction network, while \(\phi_{i,j}\) represents the characteristic diagram before the \(i\)th largest pooling layer and after the activation of the \(j\)th convolution layer.  
Figure 9: The architecture of the discriminator module.  
The GAN adversarial loss \(L^{SR}_{Gen}\) is defined by Equation (10).  
\[L^{SR}_{Gen}=\sum_{n=1}^{N}-\log D_{\theta_{D}}(G_{\theta_{G}}(L^{LR})). \tag{10}\]  
Therefore, the final total loss function is defined by Equation (11).  
\[L^{SR}=\eta L^{SR}_{\text{VGG}/ij}+\lambda L^{SR}_{Gen}+L_{1}, \tag{11}\]  
where \(\eta\) and \(\lambda\) are the weight coefficients used for balancing before different loss functions, which were set to 3 and 0.25, respectively, in our experiment.