Partial k-Space Recconstruction

In theory, most MRI images depict the spin density as a function of position, and hence should be real valued. If this were true, then by the symmetry of the Fourier transform, only half of the spatial-frequency data will need to be collected. Since real functions have conjugate symmetry in spatial frequency space, the uncollected data could be synthesized by reflecting conjugate data across the origin. Unfortunately, there are many sources of phase errors that cause the real-valued assumption to be violated. These include variations in the resonance frequency, flow, and motion. As a result, partial k-space reconstructions always require some type of phase correction, to correct for these sources of incidental phase variation. This allows real images to be reconstructed.