查看文章

GRAPPA linearly combines the undersampled k‐space signals to estimate the missing k‐space signals where the coefficients are obtained by fitting to some auto‐calibration signals (ACS) sampled with Nyquist rate based on the shift‐invariant property. 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 propose a nonlinear method to improve GRAPPA. The method is based on the so‐called kernel method which is widely used in machine learning. Specifically, the undersampled k‐space signals are mapped through a nonlinear transform to a high‐dimensional feature space, and then linearly combined to reconstruct the missing k‐space data. The linear combination coefficients are also obtained through fitting to the ACS data but in the new feature space. The procedure is equivalent to adding many virtual …