## 14 Conclusions and Perspectives for Future Research  
This work has presented a comprehensive, fully integrated framework for high-resolution MR-PET image reconstruction, combining well-established advances in structured joint sparsity, compressed sensing (CS), motion correction, blur removal, denoising, and generative adversarial networks (GANs). The proposed pipeline is the first, to our knowledge, to unify all of these components in an end-to-end optimized manner for highly undersampled, noisy, and motion-degraded MR-PET data. The validation experiments were conducted on a large and diverse dataset comprising 150 hybrid MR-PET brain scans acquired using a Siemens Biograph mMR system. The dataset included both healthy controls and patients with neuro-oncological conditions, ensuring clinical relevance. PET acquisition used a dynamic \({}^{18}\)F-FDG protocol, while MR acquisition included multi-contrast T1-weighted, T2-weighted, and FLAIR sequences. The raw data were preprocessed to simulate varying levels of undersampling (10% to 100%), motion corruption, and realistic noise patterns, enabling robust testing across clinically relevant scenarios. The entire reconstruction pipeline was implemented in Python, using PyTorch for deep learning modules. The generator and discriminator networks were trained using the Wasserstein GAN with gradient penalty (WGAN-GP) framework [19], ensuring stable adversarial training. Optimized Poisson-disc sampling for MR k-space and structured multiplexed acquisition for PET were implemented using NumPy and SciPy. The structured joint sparsity module employed efficient block Hankel matrix operations, inspired by [27; 31]. A multi-scale VoxelMorph-based motion correction network [26] was trained jointly with the super-resolution network. Extensive experiments were run on an NVIDIA A100 GPU cluster, with full training and evaluation taking approximately 96 h.  
The experimental results demonstrate that the proposed method achieves substantial improvements over both traditional and well-established baselines, including CS-MRI [8], TV regularization [66], DeepJoint [64], and advanced GAN-based and Transformer-based models [57; 60]. The framework delivers consistent gains in PSNR, SSIM, NMSE, VIF, LPIPS, and MS-SSIM metrics across all undersampling rates and motion conditions. Integrated motion correction led to a significant reduction in Target Registration Error (TRE), validating its clinical applicability. Notably, high-quality reconstructions were achieved at up to 8\(\times\) MR undersampling and 4\(\times\) PET channel reduction, offering the potential to dramatically accelerate clinical workflows. The proposed SRR pipeline addresses multiple clinical needs:  
* Reduced scan time: By enabling accurate reconstruction from sparsely sampled data, patient time in the scanner is reduced, increasing comfort and throughput. * Improved motion robustness: Joint motion correction minimizes motion artifacts, crucial for pediatric, elderly, and neurologically impaired patients. * Enhanced diagnostic value: The framework preserves fine anatomical details and functional information, supporting improved lesion detection, segmentation, and quantification. * Seamless integration: The pipeline can be deployed without major hardware modifications, facilitating clinical translation. Despite these advances, several limitations remain:
* The current framework requires paired high-resolution training data, which may not always be available. * Computational demands remain high, though this can be mitigated through model compression and hardware optimization. * Validation was focused on brain imaging; generalization to other body regions (e.g., cardiac, abdominal) warrants further study. Building on these results, several exciting directions for future research are envisioned:
* Dynamic and 4D imaging: Extending the framework to dynamic MR-PET imaging (e.g., fMRI-PET, dynamic FDG-PET pharmacokinetics) by incorporating temporal consistency and motion-aware sparsity models.