1. A method for producing a magnetic resonance image of a patient using a magnetic resonance imaging (MRI) system, the steps comprising: a) operating the MRI system to acquire a k-space image data set using a three-dimensional projection reconstruction pulse sequence that is repeated to sample k-space throughout a k-space volume having a radius R, and wherein the three-dimensional projection reconstruction pulse sequence is repeated a sufficient number of times to sample in accordance with the Nyquist condition, a central region of k-space having a radius r that is substantially smaller than the radius R but not a sufficient number of times to sample a peripheral region of k-space in accordance with the Nyquist condition; and b) reconstructing an image using substantially the entire, undersampled acquired k-space image data set and wherein the number of repetitions of the three-dimensional projection reconstruction pulse sequence is substantially less than one-half the number of repetitions necessary to fully sample the entire k-space volume in accordance with the Nyquist condition.