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

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Abstract
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. Magn Reson Med 41:179–186, 1999.