Motion correction using the k-space phase difference of orthogonal acquisitions

Abstract

Rigid body translations of an object in MRI create image artifacts along the phase-encode (PE) direction in standard 2DFT imaging. If two images are acquired with swapped PE direction, it is possible to determine and correct for arbitrary in-plane translational interview motions in both images directly from phase differences in the k-space acquisitions by solving a large system of linear equations. For example, if one assumes two N x N 2D acquisitions with in-plane translational interview motion, 4N unknown motions may corrupt the two images, but the phase difference at each point in k-space yields a system of N(2) equations in these 4N unknowns. If the acquisitions have orthogonal PE directions, this highly overdetermined system of equations can be solved to provide the motion records, which in turn can be used to correct the motion artifacts in each image. The theory of this orthogonal k-space phase difference (ORKPHAD) technique is described, and results are presented for synthetic and in vivo motion-corrupted data sets. In all cases, the data showed clear improvement of translation-induced artifacts. These methods do not require special pulse sequences and are theoretically generalizable to partial Fourier imaging and 3D acquisitions.