## 3 Implementation Based on Generative Adversarial Network (GAN)
### Experimental Setup
(iv) Description of training: During the training phase of our GAN-based implementation for the ACNCL model, the architecture was implemented on PyTorch version 24, and training was conducted on an NVIDIA GeForce RTX 2080 Ti GPU; Nvidia Corporation; California-USA, which provided the necessary computational power to handle the deep learning tasks efficiently. The Adam optimizer [34] was employed for training all networks in the experiment. The momentum parameters for Adam were set. The Momentum 1 (\(\beta\)1) of parameter 0.5 controls the exponential decay rate for the first-moment estimate (the running average of gradients). A \(\beta\)1 value of 0.5 introduces some level of smoothing by making the algorithm focus on recent gradients but not heavily weighing them, which helps avoid sharp oscillations. The Momentum 2 (\(\beta\)2) of 0.999 controls the exponential decay rate for the second moment estimate (the running average of squared gradients). With a value close to 1 (0.999), Adam efficiently captures the variance of gradients over time, leading to a more stable convergence by reducing oscillations. These settings help in controlling the moving average of gradients, where \(\beta\)1 controls the first moment (mean) and \(\beta\)2 controls the second moment (variance). The learning rate was set to 0.0002, which is a typical value for training Generative Adversarial Networks (GANs) and other deep learning models. A small batch size of 2 was chosen for training. The weights \(\lambda\)1 and \(\lambda\)2 in the equations were set to 1 and 100, respectively. The weights \(\lambda\)2 were specifically derived from the PatchGAN, which suggests an appropriate setting for discriminative networks focusing on texture and detail preservation. Weight \(\lambda\)1 was determined through a range of experiments to optimize denoising performance while maintaining the quality of tumor detection. Before training, the initial weights for convolutional layers and batch normalization layers were initialized with random numbers from a normal distribution and in this case, for convolutions, weights were sampled from N (0, 0.021) N (0, 0.021) N (0, 0.021), where the mean is 0 and the standard deviation is 0.021. For batch normalization, weights were initialized with N (1.0, 0.021) N (1.0, 0.021) N (1.0, 0.021), and biases were set to 0. The training of all networks was carried out over 300 epochs. The 300 epochs provided a balance between overfitting and underfitting; in underfitting, fewer epochs may result in overfitting. The training of the network was performed on a 100 epochs, and the training was performed on a 100 epochs. The training was performed on a 100 epochs, and the training was performed on a 100 epochs. an under-trained model, while in overfitting, training for too many epochs risks the model learning noise or irrelevant features from the training set, resulting in poorer performance on test data. By employing strategies like early stopping or weight regularization, training over 300 epochs helps achieve a good trade-off between learning enough features and avoiding overfitting. (v) Quantitative Evaluation  
The proposed algorithm was verified using a subjective analysis approach. Performance evaluators such as SSIM, PSNR, and MSE were considered to quantify the result. To evaluate the performance of the metrics of the image denoising methods, PSNR, SSIM, and MSE were used as representative quantitative measurements. 1. Peak Signal-Noise Ratio (PSNR)  
The PSNR is the ratio between the maximum possible power of a signal and the power of corrupting noise. The PSNR measures the peak signal-to-noise ratio between two images, which is used as the quality measurement between two images, the original image and the compressed image. The higher the value of the PSNR, the better the quality of the compressed image.