Iterative restoration of MR images corrupted with translational motion

Patient motion during the acquisition of magnetic resonance imaging data causes loss of resolution and ghost repetitions of the moving structures in the reconstructed image. In this paper the motion is modeled as being translational, and it is shown that this causes either the magnitude or the phase of the data to be corrupted, depending upon whether the motion is within or perpendicular to the imaging plane. The problem of restoring the image using only the corrupted data and no knowledge about the motion is addressed. The restoration problem is nonlinear in general, but is linear in two special cases. An iterative algorithm is developed that uses projections onto convex sets for magnitude retrieval and generalized projections for phase retrieval. In both cases constraint sets containing all a priori knowledge are used, and this is shown to be necessary for rapid convergence. The two algorithms may be combined to restore images corrupted by three-dimensional motion. The algorithms were verified using simulated data. © 1992.