• Christian Kames, Vanessa Wiggermann, and Alexander Rauscher.
• UBC MRI Research Centre, University of British Columbia, M10 Purdy Pavilion, 2221 Wesbrook Mall, Vancouver, BC, V6T 2B5, Canada; Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC, V6T 1Z1, Canada. Electronic address: c.kames@alumni.ubc.ca.
• Neuroimage. 2018 Feb 15; 167: 276-283.

AbstractQuantitative susceptibility mapping (QSM) is a post-processing technique of gradient echo phase data that attempts to map the spatial distribution of local tissue magnetic susceptibilities. To obtain these maps, an ill-posed field-to-source inverse problem must be solved to remove non-local magnetic field perturbations. Current state-of-the-art algorithms which aim to solve the dipole inversion problem are plagued by the trade-off between reconstruction speed and accuracy. A two-step dipole inversion algorithm is proposed to bridge this gap. Our approach first addresses the well-conditioned k-space region, which is reconstructed using a Krylov subspace solver. Then the ill-conditioned k-space region is reconstructed by solving a constrained l1-minimization problem. The proposed pipeline does not incorporate a priori information, but utilizes sparsity constraints in the second step. We compared our method to well-established QSM algorithms with respect to COSMOS in in vivo volunteer datasets. Compared to MEDI and HEIDI the proposed algorithm produces susceptibility maps with a lower root-mean-square error and a higher coefficient of determination, with respect to COSMOS, while being 50 times faster. Our two-step dipole inversion algorithm without a priori information yields improved QSM reconstruction quality at reduced computation times compared to current state-of-the-art methods.Copyright © 2017 Elsevier Inc. All rights reserved.

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