  In phase-contrast magnetic resonance imaging (PC-MRI), the velocity of spins
at a voxel is encoded in the image phase. The strength of the velocity encoding
gradient offers a trade-off between the velocity-to-noise ratio (VNR) and the
extent of phase aliasing. Phase differences provide invariance to an unknown
background phase. Existing literature proposes processing a reduced set of
phase difference equations, simplifying the phase unwrapping problem at the
expense of VNR or unaliased range of velocities, or both. Here, we demonstrate
that the fullest unambiguous range of velocities is a parallelepiped, which can
be accessed by jointly processing all phase differences. The joint processing
also minimizes the velocity-to-noise ratio. The simple understanding of the
unambiguous parallelepiped provides the potential for analyzing new multi-point
acquisitions for an enhanced range of unaliased velocities; two examples are
given.
