  Motion-compensated MR reconstruction (MCMR) is a powerful concept with
considerable potential, consisting of two coupled sub-problems: Motion
estimation, assuming a known image, and image reconstruction, assuming known
motion. In this work, we propose a learning-based self-supervised framework for
MCMR, to efficiently deal with non-rigid motion corruption in cardiac MR
imaging. Contrary to conventional MCMR methods in which the motion is estimated
prior to reconstruction and remains unchanged during the iterative optimization
process, we introduce a dynamic motion estimation process and embed it into the
unrolled optimization. We establish a cardiac motion estimation network that
leverages temporal information via a group-wise registration approach, and
carry out a joint optimization between the motion estimation and
reconstruction. Experiments on 40 acquired 2D cardiac MR CINE datasets
demonstrate that the proposed unrolled MCMR framework can reconstruct high
quality MR images at high acceleration rates where other state-of-the-art
methods fail. We also show that the joint optimization mechanism is mutually
beneficial for both sub-tasks, i.e., motion estimation and image
reconstruction, especially when the MR image is highly undersampled.
