## 2 Materials and Methods  
This study adopts an experimental research design, employing both quantitative and comparative analysis to evaluate the efficacy of the proposed ACNCL model. The research design is structured into three key phases: (i) model development and implementation using GAN-based dual-path architecture (ACNCL) and its predictors, (ii) empirical evaluation using multiple publicly available CT and MRI datasets that show results before denoising (BDn) and after denoising (ADn) and results before and after ACNCL, and (iii) benchmarking against baseline models and reference denoising methods. Each model variation (ACNCL-DnCNN, ACNCL-U-Net, ACNCL-DenseNet, ACNCL-CA-AGF, ACNCL-DWT) was trained and tested using standardized metrics (PSNR, SSIM, RMSE) and validated across cross-contextual datasets to ensure generalizability. Ablation studies further explored individual predictor contributions to the overall model's performance. The ACNCL model incorporates a variety of CNN architectures and signal processing techniques for medical image denoising and tumor detection. The model utilized the following techniques:  
1. U-Net  
U-Net is a deep learning architecture that preserves spatial details using skip connections, reducing information loss during encoding and decoding. The skip connections combine encoder and decoder features as follows:  
\[D^{\prime}_{(L-l)}=Combine\Big{(}E_{l},D_{(L-l)}\Big{)} \tag{1}\]  
where \"_Combine_\" represents concatenation (\(\oplus\)) or element-wise addition (\(+\)), ensuring the retention of spatial and contextual information for accurate segmentation. 2. DnCNN  
DnCNN is a neural network that learns residual noise in an image, making denoising more efficient by predicting noise rather than the clean image. The clean image is then reconstructed as  
\[\hat{x}=y-\hat{n} \tag{2}\]  
where \(y\) is the noisy image, \(\hat{n}\) is the predicted noise, and \(\hat{x}\) is the denoised output. DenseNet  
DenseNet enhances feature reuse and gradient flow by connecting each layer to all previous layers. The output of each layer is computed as  
\[H_{l}=F(H_{1},H_{2},\ldots,H_{l-1},x) \tag{3}\]  
where \(H_{l}\) is the feature map at the layer \(l\), \(x\) is the initial input, and \(F\) represents convolution and activation operations. Context-Aware Anisotropic Gaussian Filtering (CA-AGF)  
CA-AGF is a spatial filtering technique that adapts to local image structures, smoothing noise while preserving edges and textures. The filtered image is computed as  
\[I^{filtered}\ (p)=\sum\
olimits_{x\in N(p)}\ W(x)G_{\sigma}(x)I(x) \tag{4}\]  
where \(I(x)\) is the input image, \(G_{\sigma}(x)\) is the Gaussian kernel, and \(W(x)\) is a context-aware weight that adjusts smoothing based on local gradients. Discrete Wavelet Transform (DWT)  
DWT decomposes an image into low- and high-frequency components, enabling noise removal while preserving important structural details. The decomposition and reconstruction are expressed as  
\[ \begin{split} I\rightarrow\{L_{J},\{H_{j}\}_{j=1}^{J}\}\\ I^{\text{reconstructed}}\ =L_{J}+\sum\limits_{j=1}^{J}\ H_{j}\end{split}  \tag{5}\]  
where \(L_{J}\) represents the low-frequency approximation, preserving the main structure, while \(H_{j}\) captures high-frequency details and noise. The inverse DWT (IDWT) combines these components to reconstruct the original image with selective noise removal. Generative Adversarial Networks (GAN)  
GANs use a generator to create denoised images and a discriminator to distinguish real from fake, enhancing image quality for medical tasks like tumor detection. It is formulated as follows:  
Generator Loss (content learning):  
\[L_{G}=\mathbb{E}_{x}\Big{[}\parallel G(x)-y\parallel^{2}\Big{]} \tag{6}\]  
where \(G(x)\) is the generated clean image, and \(y\) is the target clean image. Discriminator Loss (Real vs. Fake):  
\[L_{D}=\mathbb{E}_{x}[\log D(x,y)]+\mathbb{E}_{x}[\log(1-D(G(x)))] \tag{7}\]  
where \(D(x,y)\) classifies real images, and \(D(G(x))\) classifies generated images.