## 12 Results  
The proposed joint MR-PET super-resolution framework was evaluated comprehensively on a large, clinically representative dataset comprising 150 multi-modal brain scans acquired with varying undersampling factors. The dataset comprises phantom and in vivo scans acquired on a Siemens Biograph mMR hybrid MR-PET system under institutional ethical approval. PET data were collected using \({}^{18}\)F-FDG tracers with standard brain imaging protocols, while MR employed T1-weighted sequences with TR = 2000 ms, TE = 3 ms. Motion artifacts were induced synthetically and through natural subject movement. While validated on this specific scanner model, the pipeline is adaptable to other hybrid MR-PET systems, assuming availability of raw k-space and sinogram data. Caution should be exercised when generalizing to non-brain imaging applications due to modality-specific variations. The average end-to-end reconstruction time on a system equipped with an NVIDIA A100 GPU and 256 GB RAM was approximately 18 min per full 3D volume (256 \(\times\) 256 \(\times\) 128), with breakdowns as follows: GAN inference (0.8 s/slice), motion correction (1.5 s/volume), and joint sparsity optimization (3.2 s/iteration over 20 iterations). On a mid-tier system with an RTX 3080, this time increased to 30 min. Parallelization and model pruning strategies can further reduce computation times for clinical deployment. To benchmark performance, the method was compared against classical compressed sensing approaches [8], recent deep learning architectures [57, 58, 59, 60, 61, 62, 63, 64, 65], and hybrid generative adversarial models [18, 19]. Figure 7 presents a detailed side-by-side comparison of reconstructed MR-PET brain images using multiple algorithms, including TV Regularization [66], DeepJoint [64], VoxResNet [63], DeblurGAN [49], Hybrid GAN-CS [62], TransMR-PET [57], and our proposed method. Visual inspection indicates that the proposed method yields superior anatomical clarity and reduces noise artifacts relative to competing techniques. \begin{table}
\begin{tabular}{l c c c} \hline
**Method** & **PSNR (dB)** & **SSIM** & **LPIPS** & **Diagnosis Confidence (\%)** \\ \hline GT & – & – & – & 100 \\ U-Net SRR & 29.1 & 0.841 & 0.178 & 72 \\ TV-SRR & 30.3 & 0.856 & 0.142 & 77 \\ STFNet & 31.5 & 0.879 & 0.124 & 82 \\ Diffusion SRR & 32.1 & 0.887 & 0.118 & 85 \\
**Proposed** & **33.9** & **0.914** & **0.089** & **94** \\ \hline \end{tabular}
\end{table} 
Table 1: Quantitative comparison across SRR methods. Best results in bold. The compact layout shown in Figure 8 facilitates clearer comparative visualization by minimizing inter-image whitespace while preserving all relevant anatomical details. Quantitative evaluation, as summarized in  
Tables 1-8, as well as Tables 9-11, confirms the superior Peak Signal-to-Noise Ratio (PSNR) and Target Registration Error (TRE) metrics achieved by our method, supporting the visual improvements. Statistical analyses reveal significant improvements in image quality and motion compensation, with _p_-values well below 0.005, highlighting the robustness of the proposed super-resolution and motion correction framework in clinical and phantom MR-PET datasets. The acquisition and reconstruction system is rigorously designed to satisfy the RIP conditions for the combined sampling operators [27], which ensures robustness to noise and model imperfections. The optimization is efficiently solved using proximal gradient algorithms embedded within the adversarial training framework [18; 19], unifying sparse reconstruction [8] with generative super-resolution. By harnessing these advanced sparse sampling methodologies [27], the framework achieves up to 4\(\times\) channel reduction in PET and 8\(\times\) undersampling in MR acquisitions, drastically reducing scan times and hardware complexity. Experimental results demonstrate the capability to reconstruct high-resolution MR-PET images with preserved anatomical details and functional consistency, paving the way for clinically viable, accelerated hybrid imaging.