A Combination of Nonconvex Compressed Sensing and GRAPPA (CS-GRAPPA)

Introduction Compressed Sensing (CS) (e.g. [1]) is a novel approach to reconstruct sparse undersampled datasets. Several papers (e.g. [2]) have demonstrated the benefit of CS in the field of MRI. Nonconvex CS [3] is a more recent development which allows for even higher acceleration factors and is easy to implement. A first application for dynamic cardiac imaging has been demonstrated [4]. However, these CS approaches do not take advantage of the inherent coil sensitivity information in multi-channel datasets. First formulations of CS algorithms utilizing the SENSE [5] formalism which take advantage of the coil sensitivity information in the reconstruction process have been presented (e.g. [6]). It could be shown that a combination of CS and Parallel Imaging allows for higher acceleration factors than each individual method. This work demonstrates an extension of the nonconvex CS approach from [3,4] which introduces a GRAPPA [7] reconstruction step. The advantages of this technique are that no coil sensitivity scan is necessary, and the algorithm does not need any optimized parameters to converge to the correct solution.