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 non-Cartesian trajectories; b) reconstructing coil images from the plurality of undersampled k-space data sets; c) producing coil sensitivity maps using the coil images; d) calculating a set of reference reconstruction coefficients for a coil using the undersampled coil k-space data and the coil sensitivity maps; e) calculating additional reconstruction coefficients by interpolating between calculated reference reconstruction coefficients; f) calculating additional k-space data for the undersampled k-space data set for the coil using the reference reconstruction coefficients and the additional reconstruction coefficients to form a complete coil k-space data set; g) repeating steps d), e) and f) for each coil to produce corresponding complete coil k-space data sets; h) reconstructing final coil images from the complete coil k-space data sets; and i) producing the image by combining the final coil images produced in step h).