## 3 Implementation Based on Generative Adversarial Network (GAN)
Models such as U-net and DenseNet are used to predict the underlying clean content, focusing on preserving key diagnostic features like potential tumors. The output here is the Predicted Content _(I_content1)_. Subtraction and Fusion Mechanism: The predicted noise _(I_noise)_ is subtracted from the degraded image _(I_degraded)_ to yield an intermediate prediction, which undergoes further refinement. A Fusion Mechanism then concatenates and processes the predicted content and noise through additional layers (e.g., convolutional layers and AGF extraction), producing the final predicted content _(I_content2)_.  
Tumor Detection: The tumor detection mechanism is embedded within the Generator, where the final predicted content is analyzed using specific features to identify potential tumors. DenseNet plays a key role in enhancing detection accuracy by learning complex patterns associated with tumor regions. Discriminator (PatchGAN): The Discriminator receives real and fake pairs. Real Pairs: The real content _(I_content)_ and real noise _(I_noise)_. Fake Pair: The final predicted content _(I_content2)_ and the original corrupted image _(I_degraded)_. The Discriminator evaluates the authenticity of the generated images and the accuracy of tumor detection, feeding back the results to refine the Generator's predictions. The final output from the Generator is a denoised medical image with tumor regions. The Discriminator ensures that the generated image is not only noise-free but also preserves critical diagnostic features, such as tumors, for reliable medical analysis. PatchGAN, a well-known Discriminator, targets structural inconsistencies at the patch level, addressing common issues like texture or style degradation. To tackle this problem, we incorporated PatchGAN as the Discriminator in our proposed GAN model. PatchGAN processes either a set of real images.\(\left\{I_{\text{content}},I_{\text{degraded}}\,I_{\text{noise}}\ \right\}\) or a fake image pair generated as an image set \(\left\{I_{\text{content}}\,I_{\text{degraded}}\,I_{\text{noise}}\ \right\}\) as inputs. The Generator's objective is to produce synthetic data that can deceive the Discriminator, while PatchGAN focuses on differentiating between synthetic and real data. PatchGAN is significant in medical imaging tasks because it focuses on local image patches rather than the entire image, allowing it to effectively capture fine-grained details that are crucial in medical diagnostics, such as tumor boundaries or subtle variations in tissue structures. By operating on smaller regions of the image, PatchGAN learns to differentiate between small-scale features, which is especially important in applications like tumor detection, organ segmentation, or lesion identification, where local abnormalities need to be detected with high accuracy. Figure 3: The architecture of a GAN-based implementation of the Adversarial Content–Noise Complementary Learning (ACNCL) model for image denoising and tumor detection. 2. **Loss Function:** To define the loss function, we followed the approach suggested by [31], using a combination of PatchGAN loss and L1 loss. This composite loss function, denoted as \(L_{\text{ACNCL-GAN}}\), is formulated as follows: \[L_{\text{ACNCL-GAN}}=L_{\text{GAN}}(G,D)+\phi L_{\text{L1}}(G)\] (20) where \(L_{\text{GAN}}(G,D)\) represents the GAN loss (based on PatchGAN), \(L_{\text{L1}}(G)\) is the L1 loss, and \(\phi\) is a weighting coefficient for the L1 component. The GAN loss \(L_{\text{GAN}}(G,D)\) is expressed as \[L_{\text{GAN}}(G,D)=\mathbb{E}_{x,y}[\log(D(x,y))]+\mathbb{E}_{x,y}[\log(1-D( x,G(x)))]\] (21) where \(\mathbb{E}[\cdot]\) denotes expectation, \(G\) is the Generator, \(D\) is the Discriminator, \(x\) represents the degraded image \(I_{\text{degraded,}}\) and \(G(x)\) yields the estimated noise and content components \(I^{\prime}_{\text{noise}}\) and \(I^{\prime}_{\text{content}}\). In this model, the Discriminator \(D\) seeks to maximize this objective, while the Generator \(G\) attempts to minimize it.