Modeling and reconstructing motion-corrupted MR images with applications to a beating heart

The ill-posed problem of reconstructing an animation from a set of motion-corrupted MR images is investigated. A temporal sampling model has been developed which maps each phase-encoded row of a motion-corrupted MR image to particular frames of an animation. This mapping partially fills the Fourier space of the image frames, and the remaining Fourier space is reconstructed using the projection onto convex sets (POCS) algorithm. We have tested this procedure by reconstructing an animation of a beating heart from a set of simulated motion-corrupted heart images. There is evidence to suggest that this technique may reduce the amount of data required for reconstructing an animation.