A novel relationship between the partial derivatives
of k space signal acquired using multichannel receive coils is described. It
was found that the partial derivatives of the k space signal from one coil
with respect to one direction can be expressed as a sum of partial
derivatives of signals from multiple coils with respect to the perpendicular
k space direction(s). Applications of this partial derivatives relationship
to parallel imaging reconstruction in both k space and image domains are
demonstrated.
