The two- and three-dimensional radial trajectory has been widely used due to its lower sensitivity to movement and flow and also shorter acquisition time. Re-gridding, the dominant approach for radial data reconstruction, suffers from severe artifacts at high acceleration rates. This study proposes a mathematical approach based on spherical harmonics to reconstruct images in the spherical coordinates without any interpolation in the frequency domain, unlike the conventional re-gridding algorithm. The feasibility of the proposed algorithm for reconstructing the images on both 3D Shepp-Logan and brain digital phantoms was shown.
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