1. A method for producing an image with a magnetic resonance imaging (MRI) system, the steps comprising: a) acquiring in parallel a plurality of undersampled k-space data sets with the MRI system using a pulse sequence that samples k-space along radial trajectories; b) reconstructing a corresponding plurality of low resolution images from a more densely sampled central region of each of said undersampled k-space data sets; c) producing a corresponding plurality of coil sensitivity maps from the respective low resolution images; d) producing a corresponding plurality of coil training images from the respective coil sensitivity maps; e) reconstruct a plurality of coil images using the respective coil training images and the respective undersampled k-space data sets; and f) producing an image by combining the plurality of coil images.