# Motion Correction for Brain MRI Using Deep Learning and a Novel Hybrid Loss Function
## 4 Results
### Visual Reading  
Figure 5 (left column) summarizes the readers' visual assessments of reference images, motion-corrupted images, and the MC-Net predictions against the motion magnitude for 10 selected motions each for five subjects from the \"test\" data set (simulated movements). The \"clean\" reference images were consistently scored as showing no or only minor artifacts (red lines). Conversely, the scores of the corrupted images consistently worsened with the degree of motion such that most images with \(>\)7.5 mm/\({}^{\circ}\) motion (standard deviation across scan) were rated as having \"moderate\" or \"severe\" artifacts (blue lines). The visual scores of images processed using MC-Net improved significantly for motions from [0-5] mm/\({}^{\circ}\) (\(p\) = 5 \(\times\) 10\({}^{-4}\) on Wilcoxon signed-rank test), [5-10] mm/\({}^{\circ}\) (\(p\) = 6 \(\times\) 10\({}^{-5}\)), and [10-15] mm/\({}^{\circ}\) (\(p\) = 2 \(\times\) 10\({}^{-3}\)). Importantly, even images with the most severe ranges of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Model** & **Clean Image** & **L1** & **L1 + TV** & **Two-Stage** \\ \hline SSIM & U & 1 & 0.959 \(\pm\) 0.011 & 0.961 \(\pm\) 0.009 & 0.967 \(\pm\) 0.008 \\ PSNR & U & Inf & 36.697 \(\pm\) 1.216 & 36.445 \(\pm\) 1.080 & 37.403 \(\pm\) 1.168 \\ SSIM & U + O & 1 & 0.999 \(\pm\) 0.000 & 0.999 \(\pm\) 0.001 & 0.999 \(\pm\) 0.001 \\ PSNR & U + O & Inf & 47.004 \(\pm\) 2.015 & 47.637 \(\pm\) 2.713 & 45.490 \(\pm\) 1.833 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: SSIM (mean \(\pm\) SD) and PSNR (mean \(\pm\) SD) of the motion-free images and corrected images processed using L1, L1 + TV, and the two-stage multi-loss function on test set of Dataset 1. L1 denotes models trained with L1 loss, L1 + TV denotes models trained with L1 plus TV losses in one stage, and “Two-stage” denotes models trained with L1 loss in the first stage and with L1 plus TV losses in the second stage. U represents a UNet-like structure and U + O a UNet-like structure with input-to-output concatenation [2]. Figure 4: Examples of motion artifact removal from images in the test data set of Dataset 1 using various algorithms. In (**A**) (1.90 mm/\({}^{\circ}\)), the first row contains the clean reference image, corrupted image, and motion correction results using the L1, L1 + TV, and MC-Net algorithms. The second row shows an enlarged image of 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 the 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. (**B**) The motion trajectory for (**A**), where the horizontal axis labels refer to y-position in k-space. simulated motion (\(>\)7.5 mm/\({}^{\circ}\); green versus blue lines; left column) were rated to have only \"minor artifacts\" (on average) after correction. Figure 5 (right column) demonstrates that MC-Net consistently outperformed the UNet model trained with L1-only in terms of visual image quality (paired \(t\)-tests across three raters: \(p\) = 0.009, \(p\) = 0.008, and \(p\) = 0.004). Based on the raters' assessments, the test-retest reliability (ICC and 95% confidence intervals) values are 0.91 (0.86, 0.94) for L1 loss and 0.67 (0.5, 0.79) for MC-Net. Representative results of the L1, L1 + TV, and MC-Net algorithms are shown in Figure 6. All DL methods improved image quality, but MC-Net was slightly more effective than  
Figure 5: Average motion artifact scores of test data set of Dataset 1 made by three blinded clinical readers (top to bottom for reader 1 (**A**), reader 2 (**B**) and reader 3 (**C**)) as a function of motion magnitude (x-axis). The left column shows visual scores for “clean” reference images (red lines), motion-corrupted images (blue lines), and the MC-Net predictions (green lines).