## Appendix A Details of Proposed AI Model Architecture and Process
### Training Process  
First, weights of convolutional layers were initialized using a normal distribution with a mean of 0 and standard deviation of 0.02. Binary cross-entropy loss (BCE loss) used for the GAN. It measures how well the discriminator can distinguish between real and fake images [66; 67]. Pixel-wise L1 loss used for the generator. It measures the difference between the generated image and the real image, encouraging the generator to produce realistic images [68; 69]. A weighting factor for the pixel-wise loss balanced the GAN loss and the pixel-wise loss. In the proposed model, the generator \(G\) aims to produce an output image \(G(x_{i})\) given an input condition \(x_{i}\), and the discriminator \(D\) aims to distinguish between the generated image \(G(x_{i})\) and the real target image \(y_{i}\). The total discriminator loss can be formulated as follows:  
\[L_{D}=\frac{1}{2}\Big{(}L_{real}+L_{fake}\Big{)}, \tag{1}\]  
where \(L_{D}\) is the total loss for the discriminator, \(L_{real}\) is the BCE loss for real images, and \(L_{fake}\) is the BCE loss for fake images. Each of these BCE losses is calculated using the formula for BCE loss [70; 71], which is  
\[L_{BCE}=-\frac{1}{N}\sum_{i=1}^{N}[l_{i}\cdot\log(p_{i})+(1-l_{i})\cdot\log(1- p_{i})], \tag{2}\]  
where \(N\) is the number of samples (in this case, the number of patches), \(l_{i}\) is the true label for each sample (1 for real and 0 for fake), and \(p_{i}\) is the predicted probability for each sample being real, as output by the discriminator. Applying this to the real and fake losses, \(L_{real}\) and \(L_{fake}\) can be expressed as  
\[ \begin{array}{rl}L_{real}&=-\frac{1}{N}\sum_{i=1}^{N}[\log(D(x_{i},y_{i}))], \\ L_{fake}&=-\frac{1}{N}\sum_{i=1}^{N}[\log(1-D(x_{i},G(x_{i})))],\end{array}  \tag{3}\]  
respectively [72; 73]. Here \(D(x_{i},y_{i})\) is the discriminator's output when presented with a pair of the input condition \(x_{i}\) and the real target image \(y_{i}\), and \(D(x_{i},G(x_{i}))\) is the outputwhen presented with the input condition \(x_{i}\) and the generated \(G(x_{i})\). Thus, according to the Equation (A1), the total discriminator loss is then the average of these two losses, and it is given by  
\[L_{D}=-\frac{1}{N}\sum_{i=1}^{N}[\log(D(x_{i},y_{i}))+\log(1-D(x_{i},G(x_{i})))].\] (A4)  
The total generator loss is composed of two components, which are BCE loss for generator, and pixel-wise loss. BCE loss can be calculated by using Equation (A2), similar to the discriminator's loss, but with the objective of fooling the discriminator into classifying the generated images as real. The BCE loss for the generator is given by  
\[L_{g}=-\frac{1}{N}\sum_{i=1}^{N}\log(D(x_{i},G(x_{i}))),\] (A5)  
where \(N\) is the number of samples, and \(D(x_{i},G(x_{i}))\) is the discriminator's output for the fake images generated by the generator from the input image \(x_{i}\). The generator tries to produce an image \(G(x_{i})\) that the discriminator will classify as real. The pixel-wise loss is the L1 loss, which is the mean absolute error between the generated images and the real target images. The L1 loss is given by  
\[L_{pixel}=\frac{1}{N}\sum_{i=1}^{N}|G(x_{i})-y_{i}|,\] (A6)  
where \(G(x_{i})\) is the image generated from the input image and \(y_{i}\) is the corresponding real target image. Hence, the total loss for the generator is a weighted sum of the BCE loss of the generator and the pixel-wise loss, and it can be expressed as  
\[L_{G}=L_{g}+\lambda_{pixel}\cdot L_{pixel}.\] (A7)  
For optimization, two separate Adam optimizers are used for the generator and the discriminator, known for their efficiency and adaptive learning rate capabilities [74; 75; 76]. The learning rate is set to 0.001, and hyperparameters of the Adam approach, which are beta 1 and beta 2, are set to 0.5 and 0.999, respectively. The training loop runs for a predefined number of 2000 epochs, and the dataset is iterated over in mini-batches. During each batch, the generator's gradients are zeroed out, producing a fake image from the input.