1. INTRODUCTION
Imaging artifacts due to patient motion remain a major challenge in many MRI applications. In this paper, we consider MR image reconstruction from -space data corrupted by 2D translational motion. The problem is ill-posed since there exist infinitely many image candidates and possible motions which result in the same -space data. The rigid-body motion correction problem has been an active research topic for a long time. Existing methods resolve the problem by acquiring more -space data and/or adopting a specific sampling sequence. Early works [1], [2] assume that the region of interest (ROI) is a priori known and do motion correction by borrowing the idea of phase retrieval [3]. A relatively small ROI is helpful for the motion correction and is obtained by oversampling in the frequency domain, or equivalently, imposing an enlarged field of view (FOV) in the image domain. Navigator-based methods [4], [5] have been popular in the past decade which resolve the ill-posed problem by acquiring extra -space lines named as “navigator”. The motion detected between the navigator and a motion-free reference is used for data correction. Translational motion is studied in [4] while [5] also considers rotational motion. In [6], the motion is estimated by exploiting correlations between adjacent readout lines by assuming that little motion exists during a single echotrain (the same assumption required in navigator-based methods). To guarantee the existence of the correlations, oversampling is required along the phase-encode direction [6].