We introduce a novel continuous domain compressed sensing (CD-CS) framework for the recovery of MRI data. We formulate the recovery of the high-resolution continuous domain Fourier coefficients of the image from few of its samples as a structured low-rank matrix completion problem. We also introduce novel algorithms to solve this matrix completion problem in run-times that are comparable with discrete CS formulations. The application of this algorithm to (2D+time) dynamic MRI problems is observed to yield significantly improved reconstructions compared to state of the art CS methods.
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