  This paper proposes a novel framework to reconstruct the dynamic magnetic
resonance images (DMRI) with motion compensation (MC). Due to the inherent
motion effects during DMRI acquisition, reconstruction of DMRI using motion
estimation/compensation (ME/MC) has been studied under a compressed sensing
(CS) scheme. In this paper, by embedding the intensity-based optical flow (OF)
constraint into the traditional CS scheme, we are able to couple the DMRI
reconstruction with motion field estimation. The formulated optimization
problem is solved by a primal-dual algorithm with linesearch due to its
efficiency when dealing with non-differentiable problems. With the estimated
motion field, the DMRI reconstruction is refined through MC. By employing the
multi-scale coarse-to-fine strategy, we are able to update the
variables(temporal image sequences and motion vectors) and to refine the image
reconstruction alternately. Moreover, the proposed framework is capable of
handling a wide class of prior information (regularizations) for DMRI
reconstruction, such as sparsity, low rank and total variation. Experiments on
various DMRI data, ranging from in vivo lung to cardiac dataset, validate the
reconstruction quality improvement using the proposed scheme in comparison to
several state-of-the-art algorithms.
