1. A method for producing density-compensated magnetic resonance (MR) images with a magnetic resonance imaging (MRI) system, the steps comprising; a) acquiring MR data using a rotationally symmetric acquisition trajectory; b) generating a cross-correlation matrix from the acquired MR data; c) applying a Fourier transform (FT) to the acquired MR data and the cross-correlation matrix produced in step b); d) computing a set of density-compensated, transformed MR data from the transformed cross-correlation matrix and transformed MR data produced in step c); e) applying an inverse FT to the density-compensated, transformed MR data to produce a set of density-compensated MR data; and f) performing image reconstruction on the density-compensated MR data to produce a density-compensated MR image.