Effects of polar sampling in k-space

Magnetic resonance imaging allows numerous k-space sampling schemes such as cartesian, polar, spherical, and other non-rectilinear trajectories. Non-rectilinear MR acquisitions permit fast scan times and can suppress motion artifacts. Still, these sampling schemes may adversely affect the image characteristics due to aliasing. Here, the Fourier aliasing effects of uniform polar sampling, i.e., equally spaced radial and azimuthal samples, are explained from the principal point spread function (PSF). The principal PSF is determined by assuming equally spaced concentric ring samples in k-space. The radial effects such as replication, smearing, truncation artifacts, and sampling requirements, are characterized based on the PSF.