## 3 Results  
We compared the proposed method with the image-based U-net and noniterative k-space correction methods. Figure 4 presents the reconstructed results that were obtained after ten iterations of the proposed approach using Cartesian and radial sampling masks of 10%. The first to fifth columns show the ground truth, the zero-filling, image-based U-net, noniterative, and proposed methods, respectively. The proposed method can reduce aliasing artifacts compared with the other methods. The bottom row contains the error maps obtained by different methods in comparison with the fully sampled image. Even though the image-based U-net and noniterative methods can substantially reduce artifacts, the artifacts at image edges, such as those at the boundary of structures, cannot be reduced. The proposed iterative method can reduce these artifacts as well. Table 1 shows the mean and standard deviation (SD) of the PSNR and SSIM values obtained using different methods with Cartesian and radial sampling masks of 10%. Ten iterations of the proposed method resulted in statistically significant improvements (\(p<0.001\)) in both the PSNR and SSIM compared with the other methods and the smaller iterations in the proposed method.  
Figure 3: Cartesian and radial sampling masks for the different undersampling masks—10%, 20%, 30%, and 40%—considered in this study.  
Figures 5 and 6 show the box plots of the PSNR and SSIM values obtained with Cartesian and radial sampling masks of 10%, 20%, 30%, and 40%. The columns correspond to the zero-filling, image-based U-net, and noniterative methods and each iteration of the proposed method (left to right). In each plot, the yellow line within the box represents the median; the lower and upper lines of the box represent the 25 th and 75 th percentiles, respectively; and the lower and upper adjacent lines (whiskers) represent the minimum and maximum values, respectively. Ten iterations of the proposed method outperformed the image-based U-net and the noniterative methods for all Cartesian and radial sampling masks. In addition, the SSIMs from the noniterative method with a Cartesian sampling mask  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Cartesian Sampling**} & \multicolumn{2}{c}{**Radial Sampling**} \\ \hline  & **PSNR (dB)** & **SSIM** & **PSNR (dB)** & **SSIM** \\ \hline Zero-filling & 26.31 \(\pm\) 2.13 & 0.717 \(\pm\) 0.040 & 26.45 \(\pm\) 2.16 & 0.481 \(\pm\) 0.080 \\ U-net & 28.77 \(\pm\) 1.96 & 0.859 \(\pm  
of 10% (Figure 5) and radial sampling masks of 10% and 20% (Figure 6) are lower than those from the image-based U-net and proposed methods. During training, the proposed method converges within ten iterations in terms of the PSNR and SSIM. These findings demonstrate the effectiveness of the proposed iterative method.  
Figure 5: Quantitative results in terms of PSNR and SSIM obtained by different methods for all Cartesian sampling masks. In each plot, the yellow line within the box represents the median; the lower and upper lines of the box represent the 25 th and 75 th percentiles, respectively; and the lower and upper adjacent lines (whiskers) represent the minimum and maximum values, respectively.  
Figure 6: Quantitative results in terms of PSNR and SSIM values obtained by different methods for all radial sampling masks. In each plot, the yellow line within the box represents the median; the lower and upper lines of the box represent the 25 th and 75 th percentiles, respectively; and the lower and upper horizontal lines above and below each box (whiskers) represent the minimum and maximum values, respectively.