The present invention provides a method for producing density-compensated MR images having improved signal-to-noise ratio and with reduced computational burden. The method includes sampling MR data using a rotationally symmetric acquisition trajectory, generating a cross-correlation matrix, and applying a discreet Fourier transform (DFT) to the acquired MR data and the cross correlation matrix. The method further includes employing the transformed MR data and transformed cross-correlation matrix in a linear system to produce a set of density-compensated transformed MR data, which may transformed into density compensated MR data by application of an inverse DFT. The density compensated MR data may be reconstructed by a variety of techniques to produce density compensated images.