## 3 Research Method and Materials
### Proposed Methodology  
The generative adversarial network (GAN) can produce images or samples of data that imitate the original dataset's feature distribution. There are two core components of the GAN, which are the generator and discriminator, that are trained simultaneously via a combative process. The discriminator learns how to differentiate the fake and authentic image datasets, while the generator discovers methods for producing images that look like authentic images [37]. The architecture of the GAN is depicted in Figure 3.  
The generator utilizes latent space coordinates as an input to generate a novel image. Typically, a vector with 100 numerical values represents the latent space. During the training phase, the generator learns the process of mapping each individual point in order to generate an image. Once the model has been retrained, it will acquire new mapping capabilities.  
The process of learning GANs is to perform real-time training on both the discriminator and generator networks, which is challenging and requires _min-max_ adjustments for the discriminator and generator. This process is shown in Equation (1) [38].  
\[\frac{min}{G}\frac{max}{D}\ V_{GAN}(D,G)=\mathbb{E}_{x\sim p_{data}(x)}[logD(x) ]+\mathbb{E}_{z\sim p_{z}(z)}[log(1-D(G(z)))] \tag{1}\]  
\(\mathbb{E}_{x\sim p_{data}(x)}\) is the expected value of real instances, while \(\mathbb{E}_{z\sim p_{z}(z)}\) is the expected value of fake instances. \(p_{z}(z)\) represents the random noise variable for a standard normal distribution. \(G(z)\) denotes the generator function that is responsible for mapping the data to  
Figure 2: Sample of dataset: (**A**) normal, (**B**) pneumonia, and (**C**) COVID-19.  
space, \(x\) denotes the original data, and \(D(x)\) denotes the probability of original data(\(x\)) and not the generated ones.  
It is widely acknowledged that Inception V3 is a convolutional neural network design that belongs to the Inception family. This approach incorporates various enhancements, including label smoothing, factorized 7 \(\times\) 7 convolution, and an auxiliary classifier. The Inception module initially consists of a 5 \(\times\) 5-sized convolutional layer, which is then decreased by employing two 3 \(\times\) 3 convolutions. The auxiliary classifier is employed in order to enhance the convergence of deep neural networks by mitigating the issue of vanishing gradients. Traditionally, the techniques of maximum and average polling have been employed in order to decrease the dimensions of the grid and feature map. The Inception V3 model reduces the size of the grid by performing a division operation on the current grid size, dividing it by 2. For instance, if a grid consists of a \(d\)\(\times\)\(d\) grid with k filters, the process of reduction will yield a \(d\)/2 \(\times\) 4/2 grid with 2\(k\) filters.  
The core concept of this paper is to combine DCGAN with transfer learning (Inception_V3) to acquire better chest X-ray image results. The architecture of the Inception-V3 model is depicted in Figure 4, while the proposed methodology is portrayed in Figure 5.  
Figure 4: The architecture of Inception V3 [PERSON] et al. [39].  
Figure 3: The architecture of the generative adversarial network (GAN) [37].  
Image data processing is essential to the convolutional neural network (CNN) because it will determine the classification result. The initial process is an image-resizing process that resizes the image into 288 \(\times\) 288 dimensions for training purposes, followed by image normalization. The next step will involve image augmentation using DCGAN. Then, it will continue the training process using Inception V3.