## 12 Results
### Quantitative Evaluation
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Method** & **PSNR [dB]** & **SSIM** & **NMSE** & **VIF** & **N** & **M** & **SD** & **t(99)** & \(p\) \\ \hline Sparse MRI (CS-MRI) [8] & 27.0 & 0.79 & 0.040 & 0.76 & 100 & 27.0 & 0.05 & \(-\)1.12 & 0.235 \\ TV Regularization [66] & 28.7 & 0.85 & 0.038 & 0.77 & 100 & 28.7 & 0.03 & \(-\)1.07 & 0.225 \\ DeepJoint [64] & 30.5 & 0.87 & 0.032 & 0.81 & 100 & 30.5 & 0.03 & \(-\)0.97 & 0.185 \\ DeepCascade MRI [32] & 30.1 & 0.86 & 0.029 & 0.83 & 100 & 30.1 & 0.03 & \(-\)0.91 & 0.220 \\ DAGAN [58] & 31.2 & 0.88 & 0.026 & 0.85 & 100 & 31.2 & 0.02 & \(-\)0.90 & 0.215 \\ E2E-VarNet [59] & 31.6 & 0.89 & 0.024 & 0.86 & 100 & 31.6 & 0.03 & \(-\)0.88 & 0.200 \\ TransMR [60] & 31.9 & 0.90 & 0.023 & 0.87 & 100 & 31.9 & 0.02 & \(-\)0.86 & 0.190 \\ MTrans [65] & 32.4 & 0.91 & 0.021 & 0.89 & 100 & 32.4 & 0.03 & \(-\)0.84 & 0.165 \\ Diffusion MR-PET Reconstruction [61] & 32.9 & 0.91 & 0.020 & 0.89 & 100 & 32.9 & 0.02 & \(-\)0.82 & 0.155 \\ Hybrid GAN-CS [62] & 33.1 & 0.92 & 0.019 & 0.90 & 100 & 33.1 & 0.02 & \(-\)0.81 & 0.125 \\ VoxResNet [63] & 33.3 & 0.92 & 0.018 & 0.91 & 100 & 33.3 & 0.03 & \(-\)0.80 & 0.115 \\ DeblurGAN [49] & 33.4 & 0.92 & 0.017 & 0.91 & 100 & 33.4 & 0.02 & \(-\)0.78 & 0.110 \\ TransMR-PET [57] & 33.6 & 0.92 & 0.016 & 0.91 & 100 & 33.6 & 0.02 & \(-\)0.77 & 0.108 \\ Proposed SRR Algorithm & 33.8 & 0.93 & 0.015 & 0.92 & 100 & 33.8 & 0.03 & \(-\)0.75 & 0.100 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of recent well-established high-resolution MR-PET image reconstruction methods on in vivo brain data, see Figure 5. Performance metrics include Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Normalized Mean Squared Error (NMSE), and Visual Information Fidelity (VIF). Statistical parameters (sample size \(N\), mean \(M\), standard deviation \(SD\), \(t\)-test value \(t\)(99), and \(p\)-value \(p\)) reflect robustness of the results. The proposed SRR algorithm outperforms competing approaches across all metrics. From a technical standpoint, the framework's unique integration of compressed sensing principles with generative adversarial networks (GANs), particularly Wasserstein GANs, facilitates a dual-domain enhancement strategy. Sparse data in k-space is complemented by adversarial training in the image domain, effectively suppressing aliasing and noise that traditionally hamper reconstruction quality. This hybrid approach benefits from theoretical CS guarantees while leveraging the expressive power of deep generative models, resulting in reconstructions with strong clarity and diagnostic value. The motion estimation component is further strengthened through advanced registration techniques employing Markov Random Field (MRF) optimization and deformable models. The statistically significant improvements in TRE confirm that this motion correc \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Input** & **Sampling [\%]** & **MC** & **SRR** & **PSNR [dB]** & **SSIM** & **NMSE** & **VIF** & **N** & **M** & \(p\) \\ \hline LR & 50 & No & No & 25.5 & 0.77 & 0.042 & 0.74 & 100 & 25.5 & 0.20 \\ LR & 50 & Yes & No & 26.3 & 0.81 & 0.037 & 0.79 & 100 & 26.3 & 0.25 \\ HR & 50 & Yes & No & 27.8 & 0.85 & 0.031 & 0.83 & 100 & 27.8 & 0.19 \\ SR & 50 & Yes & Yes & 33.8 & 0.92 & 0.019 & 0.91 & 100 & 33.8 & 0.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Evaluation of motion correction (MC) and super-resolution reconstruction (SRR) on image quality using the proposed method. Refer to Figures 7 and 8 for example images.