Geometrically-derived Density Compensation Function for Non-Cartesian k-space Sampling Trajectories in MRI

Motivation: A geometrically-derived density compensation function (gDCF) showed improved performance for accelerated iterative reconstruction of radial k-space data. Its simple concepts may be translatable to other non-Cartesian sampling trajectories. Goal(s): To extend gDCF to arbitrary 2D non-Cartesian sampling patterns and evaluate its performance (image quality, calculation times) in gridding and iterative reconstruction through numerical simulations. Approach: We redefined the degree of overlap calculation based on the Beurling-Landau sampling theory and evaluated the new formalism in radial, spiral and rosette trajectories and compared to other DCFs. Results: The new gDCF works for arbitrary non-Cartesian k-space trajectories and performs fast calculation times Impact: MRI acquisition using non-Cartesian sampling trajectories has potential benefits for rapid imaging and mitigating motion artifacts. The new gDCF enhances the image reconstruction of any 2D non-Cartesian MRI acquisitions, thus increasing their utility in patient scan.