A frame work for non-rigid motion corrected compressed sensing for highly accelerated MRI

Introduction: Compressed Sensing (CS) has been demonstrated to reconstruct sparse MR images of adequate quality from highly undersampled data [1], resulting in reduced scan times. In MRI, extensive motion during the acquisition (e.g. respiratory motion in cardiac scans) can cause inconsistencies in the k-space data, introducing blurring and ghosting like motion artefacts in the reconstructed images [2]. Motion correction is needed for these applications in CS MRI, not just to correct the motion related artefacts, but also to retain the sparsity level in sparse representation (such as x-f space in dynamic MRI) [3]. Recently, motion correction methods have been combined with CS to partially correct for effects of motion [4]. However, these approaches have been shown to correct for translational deformations only. In this work, we propose a novel Motion Corrected-Compressed Sensing (MC-CS) technique that incorporates a generalized motion correction formulation directly into the CS reconstruction. This technique can correct for any arbitrary non-rigid motion in the images reconstructed from CS undersampled data. The usefulness of this approach is demonstrated both in simulations and in-vivo free-breathing 2D CINE MRI, using a golden radial acquisition [5]. Results show that using this approach, a cardiac cycle free from respiratory motion, can be reconstructed with the same quality compared to that for the breath-held data. To our knowledge, the proposed approach is the first combination of CS and motion correction, where the motion information is directly incorporated into CS reconstruction.