Motion-compensated reconstruction of magnetic resonance images from undersampled data

Magnetic resonance imaging of patients who find difficulty lying still or holding their breath can be challenging. Unresolved intra-frame motion yields blurring artifacts and limits spatial resolution. To correct for intra-frame non-rigid motion, such as in pediatric body imaging, this paper describes a multi-scale technique for joint estimation of the motion occurring during the acquisition and of the desired uncorrupted image. This technique regularizes the motion coefficients to enforce invertibility and minimize numerical instability. This multi-scale approach takes advantage of variable-density sampling patterns used in accelerated imaging to resolve large motion from a coarse scale. The resulting method improves image quality for a set of two-dimensional reconstructions from data simulated with independently generated deformations, with statistically significant increases in both peak signal to error ratio and structural similarity index. These improvements are consistent across varying undersampling factors and severities of motion and take advantage of the variable density sampling pattern.