# Pocs-Augmented CycleGAN for MR Image Reconstruction
## 4 Results  
Model training took about a day, but image reconstruction only took about 5 s for one image. The SSIM and PSNR evaluations of the brain and knee test sets are demonstrated in Figure 5. The quantitative PSNR and SSIM of the first dataset are shown in Tables 1 and 2, respectively. Figure 6 shows the reconstruction results for one representative undersampled dataset. The first row shows the reconstructed images under different methods. The second row shows the difference map between the reconstructed image and the fully sampled image. Across all voxels, POCS-CycleGAN produced the smallest reconstruction errors on average, as measured by the distance to the reference. Figure 5: SSIM and PSNR evaluations of the brain and knee test set. Figure 5a,c,e shows the PSNR performance of all the assessed reconstruction methods. When compared with compressed sensing (CS), all DL-based reconstruction methods except for the CycleGAN yielded higher PSNR values (\(p<10^{-6}\), paired \(t\)-test). The POCS-CycleGAN produced a significantly higher PSNR than the CyleGAN. No significant PSNR difference was found between the POCS-CycleGAN and RefineGAN. The SSIM performances of all the methods are shown in Figure 5b,d,f. When compared with zero-filling and CS, all the DL-based methods, including U-Net, CycleGAN, RefineGAN and POCS-CycleGAN, produced higher SSIM values. All DL-based methods, including CycleGAN, produced higher SSIM values than CS. POCS-CycleGAN demonstrated the highest SSIM among these methods (\(p<10^{-6}\), paired \(t\)-tests). We show the PSNR and SSIM values of dataset 2 in Tables 1 and 2, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sampling Rate** & **10\%** & **20\%** \\ \hline U-Net & \(19.67\pm 1.89\) & \(25.11\pm 1.86\) \\ \hline GAN & \(20.51\pm 1.67\) & \(26.05\pm 1.75\) \\ \hline CycleGAN & \(21.55\pm 1.79\) & \(26.05\pm 1.82\) \\ \hline RefineGAN & \(22.83\pm 1.54\) & \(26.79\pm 1.84\) \\ \hline POCS-CycleGAN & \(24.58\pm 2.59\) & \(27.86\pm 1.92\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PSNR (mean standard deviation) of different methods with different sampling rates for the NYU dataset. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sampling Rate** & **10\%** & **20\%** \\ \hline U-Net & \(0.33\pm 0.09\) & \(0.39\pm 0.10\) \\ \hline GAN & \(0.34\pm 0.09\) & \(0.46\pm 0.10\) \\ \hline CycleGAN & \(0.38\pm 0.08\) & \(0.46\pm 0.07\) \\ \hline RefineGAN & \(0.40\pm 0.08\) & \(0.52\pm 0.08\) \\ \hline POCS-CycleGAN & \(0.42\pm 0.09\) & \(0.59\pm 0.10\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: SSIM (mean standard deviation) of different methods with different sampling rates for the NYU dataset. Figure 6: The fully sampled and undersampled brain images. The first and third rows are the brain images, and the second and fourth rows are the difference between the reconstructed image and the ground truth. The methods used for reconstructing the images are provided on top of each column. The undersampling rate was 20%, with a pseudo-random Cartesian sampling trajectory. The color bar is set between [0, 255]. The representative reconstruction results are shown in Figures 6-8. We can observe that even at the lowest sampling rate, POCS-CycleGAN preserved the structure detail very well and showed good denoising performance in both the brain and knee datasets. The proposed method outperformed the traditional compressing method and other deep learning methods. Figure 9 shows the radiologic score conducted separately by different methods over 20 subjects' brain and knee MR images. U-Net, GAN, CycGAN, RefineGAN, and POCS-CycleGAN had average scores of 2.5, 2.6, 2.8, 2.95, and 3.3 from the first radiologist and 2.15, 2.35, 2.6, 2.35, and 2.7 from the second radiologist, respectively, in terms of knee MRIs. For the brain MRIs, the corresponding 5 methods had average scores of 2.7, 3.85, 3.4, 3.6, and 3.85, respectively. Figure 8: The fully sampled and undersampled knee images.