Dynamic imaging using motion-compensated smoothness regularization on manifolds

We introduce an unsupervised deep manifold learning algorithm for motion-compensated dynamic MRI. We assume that the motion fields in a free-breathing lung MRI dataset live on a manifold. The motion field at each time instant is modeled as the output of a deep generative model, driven by low-dimensional time-varying latent vectors that capture the temporal variability. The images at each time instant are modeled as the deformed version of an image template using the above motion fields. The template, the parameters of the deep generator, and the latent vectors are learned from the k-t space data in an unsupervised fashion. The manifold motion model serves as a regularizer, making the joint estimation of the motion fields and images from few radial spokes/frame well-posed. The utility of the algorithm is demonstrated in the context of motion-compensated high-resolution lung MRI.