Method for Parallel MRI Reconstruction Based on Overlapping Low-Rank Matrix Approximations

Technology #2011-108

Parallel Imaging is a widely used strategy for accelerating MRI acquisitions. Auto-calibrated coil-by-coil methods such as GRAPPA and ARC have become increasingly popular since they do not require a separate calibration scan (as do SENSE and ASSET) nor explicit estimation of coil sensitivity profiles, making them attractive for time-limited and dynamic applications like cardiac imaging. However, this class of methods still typically requires explicit formation of a mathematical operator describing inter-coil correlations. Since this operator must itself be estimated from the measured data, its use during reconstruction unavoidably propagates error into the final generated images. To avoid this fundamental problem, recently a truly calibration- free method based on Fourier-domain low-rank matrix completion was proposed (Lustig et al, ISMRM 2010). In this work, we describe an alternative, image-domain approach for calibration-free parallel MRI reconstruction, with various advantages over the Fourier approach. In particular, our construction migrates the imposition of desired image properties out of the data observation (Fourier) domain, making it easier to extend to generalized imaging scenarios like non-Cartesian acquisitions. It is also based on local image patches, replacing a single extremely large matrix decomposition with many smaller. easily parallelisable decompositions, making extension to 3D imaging much easier.