# An Improved GAN-Based Image Restoration Method for Imaging Logging Images
## 3 Improved Imaging Logging Image Restoration Model for GAN
### Image Generation Networks
#### 3.1.1 Generating Module  
In order to better match the multi-scale feature extraction module, a fully convolutional neural network FCN was chosen as the underlying network architecture for the generation module. FCN can improve the model's ability to extract image feature information, which is very effective for image logging image restoration of complex strata. Depth separable convolution (DSConv) is combined with residual connection (RC) [17], bulk normalization (BN) [18], and the activation function LeakyReLU (LReLU) in the generation module to form a separable convolution residual block (DSCR) and inserted into the FCN network. DSConv learns continuous feature information at the image pixel level in both spatial and channel dimensions, and reduces the network parameters while retaining the learning capability of the convolutional kernel representation, thus improving the restoration efficiency of the model. RC enables the model to learn more effective boundary feature information and semantic structure information, etc., for image restoration by fusing the incoming image feature information from downsampling with the deeper feature information extracted in the moment. This accelerates the convergence of the network and improves the quality of image restoration. The structure of the deep separable convolutional residual block is shown in Figure 4.  
In order to reduce the impact of overfitting due to the large number of parameters caused by increasing the number of layers and channels per layer, the Inception module was introduced in the generation module to expand the network using convolutional kernels of size, \(1\times 1\), \(3\times 3\), and \(5\times 5\), and adding a \(1\times 1\) convolutional layer after Max Polling (MP) to reduce the number of parameters and increase the network multi-scale perceptual field. The overall network structure of the Inception module is represented in Figure 5.  
Figure 4: Deeply separable convolutional residual blocks.  
Figure 5: Structure of the Inception module.  
An overview of the network for each layer of downsampling is shown in Table 1. The model structure consists of a convolutional layer, batch normalisation, and an activation function, of which there are two types of activation functions, ReLU and LReLU. The Inception module shown in Figure 5 is introduced into the structure of layers 2 to 6 of the downsampling network, making the model more generalisable in terms of multi-scale feature extraction. After the multi-scale features are extracted, these features need to be fused for learning, so the concat operation is added specifically to the layer 4 and 6 structure for connecting the multi-scale feature extraction modules to achieve feature fusion. As the network levels deepen, DSCR is used at layers 7 and 8 to enhance the extraction of continuous feature information.  
An overview of the network for each layer of upsampling is shown in Table 2. In the upsampling operation, the feature map is continuously expanded using bilinear interpolation (BI) [19] to gradually recover the dimensions of the image. Layers 1 and 2 use the separable convolutional residual block DSCR corresponding to the downsampling; layers 3 and 5 use concat to connect the features extracted from the medium and low resolution branches to achieve the fusion of high-, medium-, and low-scale feature information; and layer 7 is paired at the end to generate the restored image using the Sigmoid activation function.