# Motion Correction for Brain MRI Using Deep Learning and a Novel Hybrid Loss Function
## 1 Introduction  
Magnetic resonance imaging (MRI) is a widely used medical imaging modality for visualizing and quantifying the anatomy and function of tissues and organs as well as pathologic processes [1]. MRI provides high spatial resolution and many different tissuecontrasts, making it superior to many other imaging modalities for detecting and characterizing soft tissue (e.g., brain, abdominal organs, and blood vessels) and pathologies. Because it involves the sequential spatial encoding of an imaging object, MRI is relatively slow and can take several minutes for a typical 3D volume scan. This prolonged image acquisition process makes MRI sensitive to motion [1; 2]. Unfortunately, motion by human subjects is unavoidable and can be caused even by involuntary physiological movements, such as respiration and cardiac motion, and unintended patient movements. Motion-induced image artifacts can drastically deteriorate image quality and reduce diagnostic accuracy [2]. For example, [PERSON] et al. reported that almost 60% of 192 clinical brain MRI scans analyzed were contaminated with motion artifacts [3]. Among these, 28% were marginally diagnostic to non-diagnostic and needed to be repeated. Because of motion-induced image artifacts, the annual loss in revenue per MR scanner can be over USD 100,000 for brain studies alone [3]. A range of prospective correction strategies have been developed to attenuate motion artifacts [4; 5; 6; 7; 8], but they commonly have limitations such as low scanner platform accessibility, applicability to specific MRI sequences only, and limitations in correcting different types of motion artifacts (e.g., in-plane versus through-plane movements). Therefore, retrospective motion correction by means of post-processing provides a good complement. One promising approach involves deep learning (DL) [1; 2; 9; 10; 11], using deep convolutional neural networks (DCNN) or other network architectures with supervised learning. Given sufficient training pairs (inputs and reference images), DCNNs can be trained to recognize the transformation from the input (motion-corrupted image) to the reference (motion-free image). Trained DCNNs have successfully been used to solve many challenging and clinically important problems, e.g., arterial spin-labeling perfusion MRI denoising [12; 13], image segmentation [14; 15], and image registration [16; 17]. DCNNs appear to be well-suited for retrospective correction of motion artifacts since there are no obvious conventional algorithms for solving this problem, and yet expert readers can \"read through\" the artifacts to some degree. Recent studies demonstrate that DCNNs can be used to attenuate motion artifacts in brain MRI scans using a data-driven approach without prior knowledge. The purpose of this study was to implement and evaluate a deep neural network architecture and loss function for motion correction. The methodology and scope of this study are different from those of previous studies. We summarize our contributions as follows. * First, a new loss function was developed, which contains an L1 component for penalizing overall image artifacts and a total variation (TV) component to penalize the loss of image details such as boundaries. Accordingly, a two-stage training strategy was implemented to first minimize the overall motion artifacts and then consider both the residual motion-induced artifacts and the loss of image details such as boundaries. * Second, the generalizability of the trained model was assessed using images with orientations and contrast different from those of the training data. * Third, to ensure rigor and demonstrate clinical utility, in-depth evaluations were made using different levels of synthetic motions and in vivo data from patients, using both objective performance indices and subjective reading conducted by experienced clinicians. Motion-free images were also used to assess potential over-corrections made by the trained DL networks.