We present a framework that has the potential to capture non-rigid 3D motion at 50 Hz, hereby drastically accelerating state-of-the-art techniques. Our model directly and explicitly relates the motion-field to the k-space data and is independent of the spatial resolution, allowing for extremely high under-sampling. We illustrate proof-of-principle validations of our method through a simulation test and whole-brain 3D in-vivo measured data. Results show that the 3D motion-fields can be reconstructed from extremely under-sampled k-space data consisting of as little as 64 points, enabling 3D motion estimation at unprecedented frame-rates.
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