Tailored utilization of acquired k-space points for GRAPPA reconstruction

The generalized auto-calibrating partially parallel acquisition (GRAPPA) is an auto-calibrating parallel imaging technique which incorporates multiple blocks of data to derive the missing signals. In the original GRAPPA reconstruction algorithm only the data points in phase encoding direction are incorporated to reconstruct missing points in k-space. It has been recognized that this scheme can be extended so that data points in readout direction are also utilized and the points are selected based on a k-space locality criterion. In this study, an automatic subset selection strategy is proposed which can provide a tailored selection of source points for reconstruction. This novel approach extracts a subset of signal points corresponding to the most linearly independent base vectors in the coefficient matrix of fit, effectively preventing incorporating redundant signals which only bring noise into reconstruction with little contribution to the exactness of fit. Also, subset selection in this way has a regularization effect since the vectors corresponding to the smallest singular values are eliminated and consequently the condition of the reconstruction is improved. Phantom and in vivo MRI experiments demonstrate that this subset selection strategy can effectively improve SNR and reduce residual artifacts for GRAPPA reconstruction.