Parallel magnetic resonance (MR) imaging uses spatial encoding from multipl
e radiofrequency detector coils to supplement the encoding supplied by magn
etic field gradients, and thereby to accelerate MR image acquisitions beyon
d previous limits. A generalized formulation for parallel MR imaging is der
ived, demonstrating the relationship between existing techniques such as SM
ASH and SENSE, and suggesting new algorithms with improved performance. Hyb
rid approaches combining features of both SMASH-like and SENSE-like image r
econstructions are constructed, and numerical conditioning techniques are d
escribed which can improve the practical robustness of parallel image recon
structions. Incorporation of numerical conditioning directly into parallel
reconstructions using the generalized approach also removes a cumbersome an
d potentially error-prone sensitivity calibration step involving division o
f two distinct in vivo reference images. Hybrid approaches in combination w
ith numerical conditioning are shown to extend the range of accelerations o
ver which high-quality parallel images may be obtained. (C) 2001 American A
ssociation of Physicists in Medicine.