Pyramidal representation of block Hankel structured low rank matrix (PRESTO) for high performance parallel MRI

In this paper, we propose a novel parallel imaging method called PRESTO (pyramidal representation of block Hankel structure low rank matrix) that do not require any calibration data but still outperform all the existing parallel imaging methods such as GRAPPA, SAKE (irregularly sampled k-space without calibration region), etc. In multi coil k-space, we reveal that the set of k-space data from several multi coils have novel annihilation properties between different coils as well as within coils. These annihilation properties lead us to a block Hankel structured matrix whose rank should be low dimensional. Accordingly, similar to SAKE, the parallel imaging problem becomes a low rank matrix completion of missing k-space data. However, unlike the SAKE, which exploits the low rankness from all k-space data or needs to combine E-SPIRiT to reduce the complexity, we demonstrate that the low rankness needs to be exploited in a pyramidal representation of block Hankel structured matrix to improve image quality as well as to reduce the complexity.

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