A 2D-GRAPPA Algorithm with a Boomerang Kernel for 3D MRI Data Accelerated along Two Phase-Encoding Directions

For the reconstruction of 3D MRI data that are accelerated along the two phase-encoding directions, the 2D-generalized autocalibrating partially parallel acquisitions (GRAPPA) algorithm can be used to estimate the missing data in the k-space. We propose a new boomerang-shaped kernel based on theoretic and systemic analyses of the shape and dimensions of the kernel. The reconstruction efficiency of the 2D-GRAPPA algorithm with the proposed boomerang-shaped kernel (i.e., boomerang kernel (BK)-2D-GRAPPA) was compared with other 2D-GRAPPA algorithms that utilize different types of kernels (i.e., EX-2D-GRAPPA and SK-2D-GRAPPA) based on computer simulation, phantom and in vivo experiments. The proposed method was validated for different sets of ACS lines with acceleration factors from four to eight and various sizes of the kernels. A quantitative analysis was also performed by comparing the normalized root mean squared error (nRMSE) in the images and the undersampled edges. Computer simulation, in vivo and phantom experiments, and the quantitative analysis, showed that the proposed method could reduce aliasing artifacts without reducing the SNRs of the reconstructed images.