Magnetic resonance imaging gridding reconstruction methods with and without density compensation functions

Reconstruction of magnetic resonance images from data not falling on a Cartesian grid is widely used for fast acquisitions, and it is a Fourier inversion problem typically solved using convolution interpolation, also known as gridding. This work presents a comparison between two gridding reconstruction methods to reconstruct magnetic resonance images from acquisitions using spiral trajectories through k-space. One method (grid-driven) is not based on a density compensation function while the other one (Direct Summation) uses Voronoi cells for the determination of the necessary areas to estimate the corresponding density compensation function. Both methods have been applied to the same image to see the reconstruction quality of each method. Both methods have correctly reconstructed the original image using only 13.73% of the original full-grid data from a Cartesian trajectory.