A kernel approach to parallel MRI reconstruction

GRAPPA has been widely used as a k-space-based parallel MRI reconstruction technique. It linearly combines the acquired k-space signals to estimate the missing k-space signals where the coefficients are obtained by linear regression using auto-calibration signals. At high acceleration factors, GRAPPA reconstruction can suffer from a high level of noise even with a large number of auto-calibration signals. In this work, we improve the GRAPPA model using a kernel approach. Specifically, the acquired k-space data are mapped through a nonlinear transform to a high-dimensional space and then linearly combined to estimate the missing k-space data. A polynomial kernel is investigated in this work. Experimental results using phantom and in vivo data demonstrate that the proposed kernel GRAPPA method can significantly improve the reconstruction quality over the existing methods.