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Motion artifacts are a pervasive problem in MRI, leading to misdiagnosis or mischaracterization in population-level imaging studies. Current retrospective rigid intra-slice motion correction techniques jointly optimize estimates of the image and the motion parameters. In this paper, we use a deep network to reduce the joint image-motion parameter search to a search over rigid motion parameters alone. Our network produces a reconstruction as a function of two inputs: corrupted k-space data and motion parameters. We train the network using simulated, motion-corrupted k-space data generated from known motion parameters. At test-time, we estimate unknown motion parameters by minimizing a data consistency loss between the motion parameters, the network-based image reconstruction given those parameters, and the acquired measurements. Intra-slice motion correction experiments on simulated and realistic 2D fast spin echo brain MRI achieve high reconstruction fidelity while retaining the benefits of explicit data consistency-based optimization.
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