Three-dimensional analytical magnetic resonance imaging phantom in the Fourier domain

This work presents a basic framework for constructing a 3D analytical MRI phantom in the Fourier domain. In the image domain the phantom is modeled after the work of Kak and Roberts on a 3D version of the famous Shepp-Logan head phantom. This phantom consists of several ellipsoids of different sizes, orientations, locations, and signal intensities (or gray levels). It will be shown that the k-space signal derived from the phantom can be analytically expressed. As a consequence, it enables one to bypass the need for interpolation in the Fourier domain when testing image-reconstruction algorithms. More importantly, the proposed framework can serve as a benchmark for contrasting and comparing different image-reconstruction techniques in 3D MRI with a non-Cartesian k-space trajectory. The proposed framework can also be adapted for 3D MRI simulation studies in which the MRI parameters of interest may be introduced to the signal intensity from the ellipsoid.