## 3 Materials and Methods
### Augmented Image Generation Using GAN  
The proposed system shown in Figure 2 generates images using a generative adversarial network. Instead of traditional square patches, we used horizontal and vertical patches. This kept global and local appearance features in the patches. A dimension of 16 \(\times\) 64 and 64 \(\times\) 16 was kept for horizontal and vertical patches, respectively. The mean intensity and variance of all the patches in the training set were extracted. All the patches were then normalized with zero mean and unit variance before being fed into the auto encoder for training.  
The idea can be implemented by using a deep learning-based generative model. Generative adversarial networks (GANs) were considered here for improving system performance by training the system intelligently. The generative adversarial network consists of two opposing networks: one is generative, and the other is discriminative in nature. These two networks race to reach the learning target for obtaining optimized results. These networks can be used to generate any distribution of data through training.  
Random inputs were used here to generate the initial set of images. The discriminator discriminates the images and assists the generator in reducing the discrimination. Through the feedback, the generator modifies the parameters and tries to generate better outputs. This can be achieved by updating loss functions. Generator and discriminator loss are updated throughout the course of process, and thereby achieve resultant images that highly resemble real ones. Thus, the network provides data with high quality for the process. CT images can be generated for various applications using these generative models [17; 18; 19; 20; 21; 22].  
The expression for standard GAN loss function is shown here. It comprises loss function of discriminator and loss function of generator. Generator tries to improve the performance, and, thereby, the loss function gets minimized. However, the discriminator functions in the reverse direction by trying to maximize the function.  
\[\text{Loss function}=\text{Ex}\left[\text{log}\left(\text{D}(\text{x}) \right)\right]+\text{EZ}\left[\text{log}\left(1-\text{D}\left(\text{G}( \text{z})\right)\right)\right] \tag{1}\]  
New realistic data can be generated with great accuracy using generative models. Here, the probability distribution of the existing dataset is used to generate the new data set. Generative adversarial network comes under this category and is used here to generate realistic data. The performance can be improved by integrating multiple generators and discriminators within the system. The GAN can also be trained in a distributed fashion, and, then, it can be presented as a multi-discriminator GAN. In GAN, as shown in the Figure 3, random images are given as the input to the generator section. From the random inputs received, the generator tries to generate sample images. The purpose of the generator section is to generate images that are identical in nature with the real images. Thus, from the random inputs, the generator generates real images as samples. These samples are fed into the discriminator. The discriminator receives real image samples as well. The function of the discriminator is to discriminate generated images from the real images. The outputs of the discriminator section, known as loss functions, are generated and classified as generator loss function and discriminator loss function.  
The signal provided by the discriminator functions acts as a feedback signal to the generator. This signal is used by the generator to update the weights. Through updating the weights of the generator, it generates images that are more identical to the real image samples. The aim of the generator is to generate images that are very much identical to the real images. This can be achieved through the updating of weights periodically. Back propagation from the discriminator helps the generator to update the weights and reproduce images with better similarity.