###### Abstract
Machine learning methods are data-driven approaches for removing or suppressing motion blur, such as using a neural style-transfer method to suppress artifacts [19] or using a motion vector prediction convolution neural network to compensate for motion blur [20]. These methods depend less on prior knowledge of motions and can reconstruct images more accurately. Although many methods have been proposed to improve the image quality of motion-blurred CT images, it is still difficult to analyze the rapid motion of aortic valves using the above-mentioned methods. These methods are limited, in that they only improve the image quality of a single blur image and do not provide motion images for motion analysis. To realize motion analysis with CT imaging, it is necessary to solve the ill-posed problem of inferring motion images from a single motion-blurred CT image. Machine learning is famous for its ability to solve ill-posed problems. For example, a deep learning neural network (DNN) in optical imaging has successfully extracted a video sequence comprising seven frames from a single motion-blurred image [21]. However, there is currently no relevant research on inferring motion images from motion blur in CT imaging. It is considered that the projection data for reconstructing a CT cross-section image corresponds to the valve motion information when each projection datum is obtained. Our central hypothesis is that information about dynamic valve motion, including opening time and maximum opening distance of the valve leaflets, can be retrieved from a single motion-blurred CT image. Since the relationship between the motion information embedded in the projection data and the resultant motion-blurred CT image is complex, we assume that a DNN can relate the motion-blurred CT image information to the corresponding time series of the valve motion information. This study aims to prove that motion images can be inferred from motion blur in CT images of aortic valves. In this case, motion blur is no longer considered an undesirable phenomenon to be removed, but a valuable source of information on the dynamics of aortic values. The in silico learning method [22] was used to prove the proposed concept, because it allows for discovering and demonstrating new concepts with a combination of the in silico dataset and deep learning. In our hypothesis, the motion information in motion-blurred CT images' is critical for achieving the goal. Therefore, to test the hypothesis, we have employed simple numerical simulation experiments with a 2D CT simulator and valve models, where a CT image was reconstructed with multiple projection data captured at different instant motion images. When a 2D CT scan is performed from the direction perpendicular to the aortic annulus, the motion of aortic valves can be approximated to 2D motion. Furthermore, to show the ability of motion blur in inferring motion images, only the motion blur in the CT images was considered in the simulation. With these simplifications, we proposed an in silico learning scheme that combined a simulation dataset and deep learning to infer 60 motion images from a single motion-blurred CT image to prove the proposed concept. To the best of our knowledge, this is the first time that this problem has been proposed and studied in the CT imaging field.