Sampling density compensation in MRI: Rationale and an iterative numericalsolution

Data collection of MRI which is sampled nonuniformly in k- space is often i nterpolated onto a Cartesian grid for fast reconstruction. The collected da ta must be properly weighted before interpolation, for accurate reconstruct ion. We propose a criterion for choosing the weighting function necessary t o compensate for nonuniform sampling density. A numerical iterative method to find a weighting function that meets that criterion is also given. This method uses only the coordinates of the sampled data; unlike previous metho ds, it does not require knowledge of the trajectories and can easily handle trajectories that "cross" in k-space. Moreover, the method can handle samp ling patterns that are undersampled in some regions of k-space and does not require a post-gridding density correction. Weighting functions for variou s data collection strategies are shown. Synthesized and collected in vivo d ata also illustrate aspects of this method. Magn Reson Med 41:179-186, 1999 . (C) 1999 Wiley-Liss, Inc.