## 2 Materials and Methods
### Gan
In DBLRNet, a GAN-based framework proposed for image deblurring, adversarial training was used to guide the generator toward producing sharp and detailed images from blurred inputs [45]. The discriminator acted as a perceptual critic, ensuring that the reconstructed images not only reduced pixel-wise error but also retained global structural realism. Compared to traditional deconvolutional approaches or purely CNN-based models, the GAN-based DBLRNet achieved superior visual clarity and edge preservation, showcasing the value of adversarial learning in handling ill-posed inverse problems. Similarly, in the deraining domain, GANs have shown strong capabilities in removing rain streaks from both static images and video frames. ESTINet, a GAN-powered deraining model published in TPAMI, utilizes a generator-discriminator pair to capture both the local texture information and the temporal consistency across frames [46]. This results in derained outputs that maintain scene integrity while effectively removing artifacts. The model's success stems from GANs' ability to model complex texture priors that are difficult to encode via traditional loss functions alone. Other notable GAN applications in low-level vision include image denoising, inpainting, and super-resolution. For example, DeblurGAN-v2 [47] achieves high-speed and high-fidelity deblurring by combining conditional adversarial loss with multi-scale content loss, producing perceptually sharper images. In another example, DID-MDN [48] introduces multi-dimensional supervision to guide GAN training for improved deraining results. In these cases, GANs often outperform traditional optimization-based techniques by producing outputs that are not only quantitatively accurate (e.g., in terms of PSNR or SSIM), but also perceptually convincing to human observers. The discriminator in these setups serves as a learned regularizer, pushing the generator to synthesize outputs that align with the manifold of natural images. This perceptual grounding is especially valuable in scenarios where standard reconstruction losses may produce overly smooth or unrealistic results. The effectiveness of GANs in these vision tasks is highly relevant to the intrusion detection domain. Both involve learning from incomplete, noisy, or imbalanced data to generate high-quality representations. Just as GANs enhance degraded images by  
Figure 2: The architectural workflow of the standard GAN. inferring structure from limited visual cues, they can similarly enhance intrusion detection training data by synthesizing plausible attack samples that improve model generalization. The underlying principle--learning from limited supervision by leveraging adversarial feedback--is shared across these domains. By drawing parallels between low-level vision tasks and intrusion detection, we highlight the broader utility and adaptability of GANs in solving real-world challenges that involve incomplete or imperfect data. Their ability to recover semantic structure, enforce perceptual fidelity, and balance underrepresented classes makes GANs a powerful tool not just in image restoration, but also in improving the robustness and performance of detection systems across diverse domains. The training objective is to reach a Nash equilibrium where the generator produces data so realistic that the discriminator cannot reliably distinguish it from real data. Mathematically, the adversarial learning objective between the generator and discriminator is formalized as shown in Equation (7) [41]:  
\[ \begin{array}{c}\underset{G}{min~{}max}\\ \underset{D}{min~{}max}\\ \underset{G}{min~{}max}\\ \underset{D}{min~{}max}\\ \end{array}