## 3 Materials and Methods
### Two Time-Scale Update Rule  
In previous research, it has been noted that the orthogonalization of the discriminator [44] can hinder the learning progress of GANs. Specifically, the process of training the orthogonalized discriminator often requires multiple updates of the discriminator for every update of the generator. To tackle this challenge, [PERSON] et al. [45] proposed a solution known as the two time-scale update rule (TTUR), which involves assigning distinct learning rates to the generator and discriminator. The TTUR approach aims to mitigate the issue of slow learning when training the orthogonalized discriminator.  
The TTUR method suggests employing fewer discriminator update steps for each generator update step whenever possible. By adopting this technique, it becomes feasible to achieve improved outcomes within the same time frame. In the context of the two time-scale update rule, the learning rates \(a(n)\) and \(b(n)\) are utilized for generator and discriminator updates, as follows:  
\[w_{n+1}= w_{n}+b(n)(g(\theta_{n},w_{n})+M_{n}^{(w)}) \tag{8}\] \[\theta_{n+1}= \theta_{n}+a(n)(h(\theta_{n},w_{n})+M_{n}^{(\theta)}),\]  
where \(w\) and \(\theta\) represent the parameter vectors of the discriminator \(D(.,w)\) and the generator \(G(.,\theta)\), respectively. In addition, \(g(\theta.w)\) and \(h(\theta,w)\) indicate the true gradient of the discriminator and generator, and \(M^{(w)}\) and \(M^{(\theta)}\) are random variables.  
\begin{table}
\begin{tabular}{c c c} \hline
**Input Image Size** & **Convolution Operation** & **Output Image Size** \\ \hline \(3\times 256\times 256\) & Conv2d:16 3 \(\times\) 3 stride = 2 & 16 \(\times\) 256 \(\times\) 256 \\  & (BN SN 0.2 leakyReLU & \\  & Dropout) & \\
16\(\times\)256 \(\times\) 256 & Conv2d:32 3 \(\times\) 3 stride = 2 & 32 \(\times\) 256 \(\times\) 256 \\  & (BN SN 0.2 leakyReLU & \\  & Dropout) & \\
32 \(\times\) 256 \(\times\) 256 & Conv2d:64 3 \(\times\) 3 stride = 2 & 64 \(\times\) 256 \(\times\) 256 \\  & (BN SN 0.2 leakyReLU & \\  & Dropout) & \\
64 \(\times\) 256 \(\times\) 256 & Conv2d:128 3 \(\times\) 3 stride = 2 & 128 \(\times\) 256 \(\times\) 256 \\  & (BN SN 0.2 leakyReLU & \\  & Dropout) & \\
128 \(\times\) 256 \(\times\) 256 & Flatten (Liner Sigmoid) & 1 \(\times\) 262,144 \\ \hline \end{tabular}
\end{table}
Table 2: Detailed information of the proposed discriminator.  
The flowchart presented in Figure 6 illustrates the proposed approach, which progresses through four distinct steps. Firstly, the integration of the self-attention module occurs in both the low-dimensional and high-dimensional convolutional layers of the generator. This integration plays a crucial role in generating the synthetic data. Secondly, spectral normalization is employed to train both the generator and the discriminator. The discriminator evaluates the authenticity of both the synthetic and real data. Thirdly, different learning rates are assigned to the generator and discriminator. Lastly, a cyclic training process is executed for the discriminator and generator, continuously improving the quality of the synthesized images until a state of Nash equilibrium has been achieved. The losses associated with the generator and discriminator guide the parameter updates in their respective networks.