Sampling density compensation in MRI: Rationale and an iterative numerical solution

Data collection of MRI which is sampled nonuniformly in k-space is often interpolated onto a Cartesian grid for fast reconstruction. The collected data must be properly weighted before interpolation, for accurate reconstruction. We propose a criterion for choosing the weighting function necessary to 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 methods, it does not require knowledge of the trajectories and can easily handle trajectories that "cross" in k-space. Moreover, the method can handle sampling patterns that are undersampled in some regions of k-space and does not require a post-gridding density correction. Weighting functions for various data collection strategies are shown. Synthesized and collected in vivo data also illustrate aspects of this method.