Current research in MRI is based on using CS implications to reconstruct high-quality images from a subset of $$$k$$$-space data acquired in an incoherent manner. In this work, we introduce a mathematical framework for improving undersampled MRI data reconstruction, which we call CS+M, where M stands for motion. The significance here, and unlike existing solutions is that by modeling explicitly and simultaneously the inherent complex motion patterns, given by physiological or involuntary motion, in a CS setting, synergies in a complex variational problem are created. These synergies have clinical potentials in terms of improving image quality while reducing motion artifacts.
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