Motion Correction from Orthogonal k-Space Phase Difference

Introduction It is well known that rigid body translations of an object in MRI will create image artifacts along the phase encode (PE) direction in standard 2-D FT imaging [1]. Methods have been proposed to take advantage of the directionality of the artifacts to improve image quality by combining images with dissimiliar artifact patterns. Two such methods are the orthogonal correlation algorithm (ORCA) [2] and oblique k-space scan (OKscan) [3]. Neither technique attempts to deduce the actual motion record or to correct the k-space phase modulation caused by the motion. Building upon the ORCA technique which acquires two images with swapped PE direction, it is possible to determine motion and to correct the raw data using the orthogonal kspace phase difference (ORKPHAD) of the two scans. If one assumes 2-D in-plane interview motion, 4N unknown motions may corrupt the two NxN images. The ORKPHAD yields N2 equations involving only 4N unknowns. After the phase difference is properly unwrapped, the motion records can be found by a weighted least squares inversion of the system of equations. Phase corrections for the deduced motions can then be applied to correct the motion-corrupted images. This work demonstrates ORKPHAD on simulated phantom image corruptions. Methods Two forms relating the k-space phase difference to the motion records are given in Eqs. (1) and (2). In Eq. (1), the phase difference at the (m,n) position in k-space is the sum of four terms. The 1xN vector k