# Motion Correction for Brain MRI Using Deep Learning and a Novel Hybrid Loss Function
## 4 Results
### Cross-Dataset Generalization  
To assess cross-dataset generalization, we first applied the MC-Net algorithm (which was trained using axial images only) to sagittal and coronal T1-weighted slices with simulated motion artifacts. The mean SSIMs of sagital and coronal slices improved from 0.64 and 0.71 to 0.75 and 0.84, respectively. The mean PSNRs of sagital and coronal slices improved from 24.03 and 24.55 to 24.40 and 25.37, respectively. Representative results from two different scans are shown in Figure 7. The images from the first subject (Figure 7A,B; 3.95 mm/\({}^{\circ}\)) show mild to moderate motion artifacts. The SSIM values are similar for the two views, both before (0.83 and 0.84) and after the elimination of artifacts using MC-Net (0.87-0.9). The PSNR values for the two views are 28.22 and 28.01, and those after artifact removal using MC-Net are 28.85 and 28.76. The images from the second subject (Figure 7, bottom row; 5.99 mm/\({}^{\circ}\)) show moderate to severe motion artifacts, and the SSIM values improved from 0.49 to 0.73 (sagittal) and 0.68 to 0.84 (coronal). The PSNR values improved from 22.00 to 23.50 (sagittal) and 24.18 to 25.29 (coronal). Overall, these improvements in SSIM scores after processing with MC-Net are consistent with those observed for axial scans (regression lines in Figure 3).  
Figure 6: Examples of motion artifact removal from images in the test data set of Dataset 1 using various algorithms. In (**A**) (6.04 mm/\({}^{\circ}\)) and (**B**) (4.67 mm/\({}^{\circ}\)), the first row of each subfigure contains the clean reference image, corrupted image, and motion correction results obtained using the L1, L1 + TV, and MC-Net algorithms. The second row of each subfigure zooms in on the red rectangle. The SSIM and PSNR values for each corrected image (relative to the “clean” image) are also shown (bottom row). The third row shows the error maps between reference (i.e., clean image) and corrupted image and motion correction results. The difference between each pixel shown in the error maps was multiplied by a factor of five. (**C**,**D**) show the motion trajectories for (**A**,**B**), where the horizontal axis labels refer to y-positions in k-space.  
To assess the ability of the MC-Net algorithm to correct motion artifacts in T2-weighted images, we randomly selected and corrupted 264 slices with FLAIR contrast (Dataset 3). The SSIM and PSNR of the corrupted images were 0.69 \(\pm\) 0.11 and 26.15 \(\pm\) 2.72 (mean \(\pm\) SD), and they were 0.67 \(\pm\) 0.04 and 25.25 \(\pm\) 1.54 after correction. Thus, processing with MC-Net slightly decreased image quality. This finding was  
PSNR values were poorer after the images were processed using MC-Net, and slight banding artifacts appeared. Conversely, when MC-Net was applied to a FLAIR image with more-severe motion artifacts (Figure 8B, 14.85 mm/\({}^{\circ}\)), the SSIM and PSNR values improved (from 0.55 to 0.63 and from 22.14 to 23.12, respectively). However, despite these apparent improvements, the highlighted region of the \"corrected\" image provides a poor representation of the original scan; in fact, new (false) anatomical \"features\" appear in the \"corrected\" image.