1. A method for producing an image with a magnetic resonance imaging (MRI) system, the steps comprising: a) arranging a three-dimensional (3D) k-space along a Cartesian grid of points; b) dividing k-space into a central region of k-space and a peripheral region of k-space; c) selecting points in k-space within a plurality of radial vanes that extend radially outward from the central region of k-space through the peripheral region of k-space as viewed in a plane sampled by two phase encoding gradients to create a plurality of gaps between the radial vanes that is substantially a factor of N times greater in area than the radial vanes; d) acquiring, with an MRI system having arrays of RF receiver coils, NMR signals from a subject to fully sample the central region of the 3D k-space and undersample the peripheral region of k-space by only sampling k-space within the plurality of radial vanes; and e) reconstructing an imaging of the subject using the acquired NMR signals.