• Carlos Milovic, Berkin Bilgic, Bo Zhao, Christian Langkammer, Cristian Tejos, and Julio Acosta-Cabronero.
• Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile.
• Magn Reson Med. 2019 Feb 1; 81 (2): 1399-1411.

PurposeBackground-field removal is a crucial preprocessing step for quantitative susceptibility mapping (QSM). Remnants from this step often contaminate the estimated local field, which in turn leads to erroneous tissue-susceptibility reconstructions. The present work aimed to mitigate this undesirable behavior with the development of a new approach that simultaneously decouples background contributions and local susceptibility sources on QSM inversion.MethodsInput phase data for QSM can be seen as a composite scalar field of local effects and residual background components. We developed a new weak-harmonic regularizer to constrain the latter and to separate the 2 components. The resulting optimization problem was solved with the alternating directions of multipliers method framework to achieve fast convergence. In addition, for convenience, a new alternating directions of multipliers method-based preconditioned nonlinear projection onto dipole fields solver was developed to enable initializations with wrapped-phase distributions. Weak-harmonic QSM, with and without nonlinear projection onto dipole fields preconditioning, was compared with the original (alternating directions of multipliers method-based) total variation QSM algorithm in phantom and in vivo experiments.ResultsWeak-harmonic QSM returned improved reconstructions regardless of the method used for background-field removal, although the proposed nonlinear projection onto dipole fields method often obtained better results. Streaking and shadowing artifacts were substantially suppressed, and residual background components were effectively removed.ConclusionWeak-harmonic QSM with field preconditioning is a robust dipole inversion technique and has the potential to be extended as a single-step formulation for initialization with uncombined multi-echo data.© 2018 International Society for Magnetic Resonance in Medicine.

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