# Motion Correction for Brain MRI Using Deep Learning and a Novel Hybrid Loss Function
## 5 Discussion  
The goal of our work was to develop a DL-based automated method for eliminating or attenuating motion artifacts in brain MRI scans. The resulting MC-Net network uses a novel loss function and a novel training strategy and was trained and tested using data involving a wide range of real movements. A series of comprehensive evaluations were performed to assess the risk of over-correction and generalizability. The former was assessed by inputting the motion-free images and assessing how well the quality of images was preserved after being processed by MC-Net. The latter was assessed through testing MC-Net on a different dataset with different image orientations and image contrasts.  
As in previous work [2; 9; 34], MC-Net was able to correct motion artifacts in brain scans. We based our work on a customized UNet-like auto-encoder architecture [35] that is widely used in medical image analysis. This network architecture is complex enough to perform motion correction but also simple enough to benefit from the hybrid loss function. The proposed hybrid loss and two-stage training was slightly better in terms of improving final image quality than approaches with single-stage training, e.g., the L1 loss used in a prior study [2], and was especially beneficial for correcting severe motion artifacts. Due to the short processing time per image (40 ms), implementation using the open-source framework Keras [29] with GPU acceleration should allow real-time motion correction.  
We base the comparison of our results to those from other studies on the SSIM, since it is commonly used to assess the performance of deep learning algorithms for brain/head MRI motion correction. Also, it is important to consider that SSIM values and improvements are dependent upon the degree of motion corruption (Figure 3). The first comparison paper [34] had pre- and post-correction SSIM values of 0.863 (suggesting moderate motion) and 0.924; the improvement approximately matches that of MC-Net. The second comparison paper [19] reports SSIM values of 0.795 (corrupted) and 0.862 (corrected), suggesting an improvement somewhat below that achievable with MC-Net (based on the linear regressions in Figure 3). Finally, a third paper [1] found an improvement  
Figure 9: Examples of images with real motion (non-simulated) artifacts from Dataset 4. From left to right (**A–C**), the severity of motion artifacts increases. Each set shows the original motion-corrupted image (left) and outputs from MC-Net (right). The second row shows a magnification of the region of interest (ROI) within the red rectangle. The third row shows the error maps between network input (i.e., corrupted image) and MC-Net prediction. The difference between each pixel shown in the error maps was multiplied by a factor of five.  
in SSIM from 0.68 to 0.92. The pre-correction value of 0.68 suggests substantial motion artifacts and is in fact outside the range assessed by our simulations (lowest value is 0.75). Overall, the improvement in SSIM between the motion-corrupted images (0.773) and the motion-corrected results (0.919) from MC-Net is better than that of the first two studies but smaller than that achieved by the model proposed in [1]. The greater improvement of the model may be a result of integrating the pre-trained VGG [36] as a main building block of the DL model. By using the pre-trained VGG, the DL model can benefit from transfer learning, which has been shown to boost performance for other medical imaging or computer vision tasks, such as in [10; 13; 14; 37]. Conversely, we trained our initial model from scratch.