A method for reconstructing an image from undersampled, parallel MRI data sets acquired with a pulse sequence that samples k-space along radial trajectories includes the synthesis of training k-space data from the acquired data. The training k-space data is produced by reconstructing training images from the fully sampled, central k-space region of the acquired MRI data sets, and the training k-space data is used in a radial GRAPPA image reconstruction method to produce an image frame.