## 2 Materials and Methods
### Adversarial Content-Noise Complementary Learning (ACNCL)  
Under ACNCL (Adversarial Content-Noise Complementary Learning), we tackle the problem of denoising medical images, particularly CT and MRI scans, by leveraging an innovative approach that incorporates GANs as key components in learning both content and noise features simultaneously. This model combines both noise and content prediction, ensuring improved denoising while preserving structural details critical for medical diagnosis. Consider an image denoted as \(I_{\text{degraded}}\) which has been compromised by noise due to low-dose imaging or under-sampling techniques. The corresponding high-quality image, free from such degradation, is represented as \(I_{\text{content}}\). In the context of deep learning-based denoising for medical images, \(I_{\text{degraded}}\) can be conceptualized as the sum of its undistorted sub-content \(I_{\text{content}}\) and the additive noise component \(I_{\text{noise}}\):  
\[I_{\text{degraded}}\ =I_{\text{content}}\ +I_{\text{noise}} \tag{16}\]  
(a) Noise Identification and Context Partitioning: The denoising process begins with the Noise Identifier (ACNCL-Part 1), which detects the noise type present in the input image \(I_{\text{degraded}}\). Noise in medical images often arises due to low-dose imaging or under-sampling techniques, which can obscure crucial features. A Context Partitioning step follows, where noisy images are separated based on the extent and type of noise, allowing for tailored reconstruction. This partitioning facilitates efficient denoising by focusing on relevant noise patterns in each image segment. (b) Content and Noise Prediction: In the denoising model, content prediction aims to recover the underlying noise-free image \(I_{content}\). Given a degraded input image \(I_{\text{degraded}}\), we obtain a predicted clean image \(I^{\prime}_{\text{content}}\) by applying a content predictor \(p_{c}\):  
\[I^{\prime}_{content}=\text{p}_{c}\big{(}I_{degraded}\big{)} \tag{17}\]  
In contrast, Residual Mapping (noise prediction) estimates the noise component. \(I^{\prime}_{noise}\). The clean content can then be derived by subtracting this predicted noise from \(I_{\text{degraded}}\) :  
\[I^{\prime}_{content}=I_{degraded}-I^{\prime}_{noise}=I_{degraded}-p_{n} \big{(}I_{degrad}\big{)} \tag{18}\]Here, \(p_{n}\) represents the noise predictor, and \(l^{\prime}_{\text{noise}}\) is the estimated noise component. This approach balances consistency and detail preservation by combining the strengths of both content and noise prediction. (c) Adversarial Content-Noise Complementary Learning (ACNCL) Integration: The ACNCL model harmonizes the outputs of \(p_{c}\) (content predictor) and \(p_{n}\) (noise predictor), framing denoising as an end-to-end learning task. The final predicted content image \(I^{\prime}_{content}\) is generated using a fusion function \(f\) that combines the outputs from content and noise prediction:  
\[ \begin{split}& I^{\prime}_{\text{content}}\,=G\Big{(}I_{\text{ degraded}}\Big{)}=f\big{(}I^{\prime}_{\text{content}\,1}\,,I^{\prime}_{\text{content}\,2}\big{)}=\\ & f\Big{(}p_{c}\Big{(}I_{\text{degraded}}\Big{)}\,,I_{\text{ degraded}}-p_{n}\Big{(}I_{\text{degraded}}\Big{)}\Big{)}\end{split}  \tag{19}\]  
Here, \(I^{\prime}_{content1}\) and \(I^{\prime}_{content2}\) represent the outputs from the content predictor and the noise-derived content, respectively. The fusion function \(f\) integrates both predictions to yield the final denoised result. In the ACNCL denoising model for image denoising and tumor detection in low-quality images, we utilized two training pairs derived from each image as shown in Figure 1:  
Figure 1: Adversarial Content-Noise Complementary Learning (ACNCL) denoising architecture for image denoising and tumor detection in low-quality medical images. * The pair \(\left\{I_{\text{degraded}}\,,I_{\text{content}}\right\}\) is used to train the content predictor \(p_{c}\), focusing on reconstructing clean content.