# An Improved GAN-Based Image Restoration Method for Imaging Logging Images
## 4 Training the Improved GAN Model
### Loss Function  
The overall performance of the imaging logging image restoration model is not only dependent on the network structure, but the selection of the loss function is also critical. During model training, the aim is to use the loss function values as feedback to drive the model to convergence, so the model training goal is to minimise the loss function values. In order to better restore the texture details and semantic structure of the imaging logging images, this paper uses a combination of content loss, perceptual loss, style loss, and adversarial loss to train an improved GAN model. In this paper, we use a combination of content loss, perceptual loss, stylistic loss, and adversarial loss as a loss function for image restoration, mainly to combine different types of information in order to improve the effectiveness of image restoration. For this, a pixel-level difference metric is used to measure the similarity between the restored image and the original image. By minimising content loss, the restored image can more closely resemble the original image, retaining more of the original detail and structure. Perceptual loss uses a pre-trained deep learning model (VGG network) to extract high-level features of the image, which are used to compare the perceptual differences between the restored image and the original image. Perceptual loss can help ensure that the restored image is more perceptually realistic and avoids generating false details. Style loss is used to compare the restored image with the original image in terms of style. By minimising style loss, the restored image retains the texture and style of the original image, increasing visual consistency. Adversarial loss introduces the concept of an adversarial generative network in which the generator tries to deceive the discriminator, which in turn tries to distinguish between the real image and the generated image. By minimising adversarial loss, the restored image can be more realistic and have higher visual quality. Combining these different types of loss functions can enable image restoration models to produce more realistic and natural-looking restoration results while maintaining structural and content realism. Each loss function is described below. Content loss: Content loss consists of the loss of intact regions \(L_{\varphi}\) and the loss of missing regions \(L_{h}\). Since \(L_{1}\) loss ignores the structural correlation between missing and undamaged regions, multi-scale structural similarity MS-SSIM [23] is used to better preserve the contrast of information in high frequency regions of the image. The content loss consists of \(L_{1}\) loss and MS-SSIM, which is calculated as shown in the equation below:  
\[L_{\varphi}=(1-a)\|M_{in}\odot(I_{g}-I_{t})\|_{1}+a(1-MS_{M})(M_{in}\odot(I_{g }-I_{t})) \tag{12}\]  
\[L_{h}=(1-a)\|(1-M_{in})\odot(I_{g}-I_{t})\|_{1}+a(1-MS_{M})((1-M_{in})\odot(I_ {g}-I_{t})) \tag{13}\]  
where \(M_{in}\) represents the mask region, \(\odot\) denotes the Hadamard product, \(MS_{M}\) denotes MS-SSIM (the formula can be found in Equation (16)), \(I_{g}\) denotes the image generated by the generative network, \(I_{t}\) denotes the real image, and the constant \(a\) is used to balance the MS-SSIM loss and the \(L_{1}\) loss, with a value defined empirically as 0.5 in the model. Perceptual loss: Perceptual loss is introduced in order to give the generated image a higher level of structural similarity to the real image, rather than just making the generated image a pixel match to the real image. Perceptual loss can be used to obtain a higher level of structural information using convolutional layers to perceive images from higher latitudes closer to the level of human visual effects. This paper introduces the perceptual loss defined on a VGG16 network pre-trained on ImageNet, which is calculated as follows:  
\[L_{prec}=\frac{1}{N}\sum_{i=1}^{N}\|F^{i}(I^{t})-F^{i}(I^{g})\|^{2} \tag{14}\]  
where \(N\) denotes the image size and \(F^{i}(\cdot)\) denotes the feature map of the ith pooling layer.