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PURPOSE: To investigate systematic errors in traditional quantitative susceptibility mapping (QSM) where background field removal and local field inversion (LFI) are performed sequentially, to develop a total field inversion (TFI) QSM method to reduce these errors, and to improve QSM quality in the presence of large susceptibility differences. THEORY AND METHODS: The proposed TFI is a single optimization problem which simultaneously estimates the background and local fields, preventing error propagation from background field removal to QSM. To increase the computational speed, a new preconditioner is introduced and analyzed. TFI is compared with the traditional combination of background field removal and LFI in a numerical simulation and in phantom, 5 healthy subjects, and 18 patients with intracerebral hemorrhage. RESULTS: Compared with the traditional method projection onto dipole fields+LFI, preconditioned TFI substantially reduced error in QSM along the air-tissue boundaries in simulation, generated high-quality in vivo QSM within similar processing time, and suppressed streaking artifacts in intracerebral hemorrhage QSM. Moreover, preconditioned TFI was capable of generating QSM for the entire head including the brain, air-filled sinus, skull, and fat. CONCLUSION: Preconditioned total field inversion improves the accuracy of QSM over the traditional method where background and local fields are separately estimated. Magn Reson Med 78:303-315, 2017. © 2016 International Society for Magnetic Resonance in Medicine.
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