1. A method of parallel magnetic resonance imaging comprising: a) sequentially and separately generating magnetic gradient encoding fields in an imaging region; b) sequentially acquiring echo data representing signal intensities; c) computing a reconstructed image from the acquired echo data; and d) displaying the computed image; wherein the sequentially acquired echo data corresponds to the sequentially generated magnetic gradient encoding fields; wherein multiple receiver coils are used to simultaneously acquire echo data at each instant in time; wherein the multiple receiver coils have corresponding nonuniform receiver coil sensitivity profiles; wherein the magnetic gradient encoding fields are nonlinear spatial gradient fields that are solutions to the Laplace equation; and wherein the magnetic gradient encoding fields approximate ideal gradient field shapes that are optimally complementary to spatial information provided by the receiver coil sensitivity profiles.