Derivative Encoding for Parallel Imaging

Jun Shen¹

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.