Analytical Fourier transforms (FT), such as FT of 2D and 3D
Shepp-Logan phantoms, enable accurate arbitrary k-space sampling of digital
phantoms. Here, we present and demonstrate a computationally efficient MATLAB
implementation of the analytical FT of polyhedral phantoms with uniform
intensity or non-uniform intensities. The computation time of the
implementation is presented, as well as demonstrations showing its feasibility of simulating physiologically
relevant phantoms and evaluating non-Cartesian sampling trajectories and
parallel imaging algorithms. The implementation is now available through the
Mathworks user community and GitHub.
