Magnetic Resonance Imaging allows high resolution data acquisition with the downside of motion sensitivity due to relatively long acquisition times. Even during the acquisition of a single 2D slice, motion can severely corrupt the image. Retrospective motion correction strategies do not interfere during acquisition time but operate on the motion affected data. Known methods suited to this scenario are compressed sensing (CS), generative adversarial networks (GANs), and explicit motion estimation. In this paper we propose an iterative approach which uses GAN predictions for motion estimation. The motion estimates allow to provide data consistent reconstructions and can improve reconstruction quality and reliability. With this approach, a clinical application of motion estimation is feasible without any further requirements on the acquisition trajectory i.e. no temporal redundancy is needed. We evaluate our proposed supervised network on motion corrupted HASTE acquisitions of brain and abdomen.
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