Parallel Imaging Acceleration beyond Coil Limitation using a k-space Variant Low-rank Constraint on Correlation Matrix

This work introduces a mathematical model that converts k-space parallel imaging into the function of a low-rank Toeplitz-like correlation matrix formed from auto- and cross-channel correlation functions. By applying a k-space variant low-rank constraint to this correlation matrix, missing data can be reconstructed in a region-by-region fashion. Imaging acceleration can be improved if a higher undersampling factor is used in those regions with a more stringent constraint. It is demonstrated that this approach permits the use of a net acceleration factor higher than the number of coil elements in the phase-encoding direction.

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