## 1 Introduction
Recent innovations such as Multi-Level Densely Connected Super-Resolution Networks (mDCSRN) [16] and generative adversarial networks (GANs) [17; 18; 19] have mitigated some of these issues by promoting realistic texture synthesis and enhancing edge preservation. GANs, first introduced by [PERSON] et al. [17], employ a competitive training framework between a generator and discriminator network, yielding well-established super-resolution results by minimizing perceptual and adversarial losses. Nonetheless, GANs require careful design to avoid introducing artifacts or noise amplification [11]. Generative adversarial networks (GANs) serve a pivotal role in addressing the inherent challenges of MR-PET fusion. By leveraging adversarial and perceptual loss functions, GANs effectively mitigate modality-specific artifacts, enhance anatomical detail, and enforce cross-modality consistency. This is particularly beneficial for aligning the high spatial resolution of MR with the metabolic specificity of PET, enabling coherent, realistic reconstruction from severely degraded or undersampled data. Previous efforts in MR-PET joint reconstruction include dictionary-based priors, convolutional neural networks (CNNs) for modality translation, and joint regularization using total variation or low-rank priors. Approaches such as DeepMR-PET [20], CoMoGAN [21], and JTV-based reconstruction [22] have demonstrated the benefits of shared anatomical priors and learned fusion strategies. However, these techniques often lack robustness to motion and undersampling, which our GAN-augmented approach addresses explicitly. Beyond image-domain techniques, effective MR-PET reconstruction requires addressing raw data challenges [23]. Efficient k-space sampling, leveraging Hermitian symmetry and Partial Fourier methods [24], reduces acquisition time by reconstructing missing data while maintaining image fidelity. Integration of k-space corrections with GAN-based frameworks has shown promise [25]in improving reconstruction quality beyond conventional methods. Additionally, motion artifacts, a significant source of image degradation especially in PET, can be effectively mitigated via deformable motion estimation integrated into the reconstruction pipeline [26]. This work introduces a comprehensive framework for MR-PET image reconstruction that synergistically combines the following:  
* Sparse k-space and sinogram acquisition optimized via advanced sampling strategies [8];
* Structured joint sparsity constraints to maintain anatomical consistency between MRI and PET modalities [27];
* A generative adversarial network incorporating multilevel features to enhance super-resolution reconstruction [11; 16];
* An integrated deformable motion compensation module to correct patient movement artifacts [26];
* Discrete preprocessing stages tailored for deblurring, denoising, and artifact suppression [28]. The key contributions of this work include:  
1. A novel generative super-resolution approach explicitly designed for multimodal MR-PET data fusion, capable of capturing multi-scale anatomical features. 2. A joint sparsity-driven reconstruction framework that harmonizes MRI and PET raw data, improving structural coherence [27]. 3. Advanced k-space sampling and correction techniques leveraging compressed sensing and partial Fourier symmetry [8; 24] to accelerate acquisition without compromising resolution. 4. Integration of a well-established deformable motion estimation procedure [26] within the reconstruction pipeline to mitigate motion-induced artifacts. 5. A modular preprocessing strategy addressing denoising and deblurring challenges [28] to enhance overall image quality. 6. Extensive validation on clinical and phantom datasets, confirming improvements over existing well-established methodologies [16; 26]. This integrated methodology sets a new standard for rapid, high-fidelity MR-PET imaging, promising to advance both research and clinical applications in neuro-oncology and beyond.