Rapid two-step dipole inversion for susceptibility mapping with sparsity priors

Neuroimage. 2018 Feb 15;167:276-283. doi: 10.1016/j.neuroimage.2017.11.018. Epub 2017 Nov 11.


Quantitative 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.

Keywords: Dipole inversion; Fast reconstruction; Quantitative susceptibility mapping; Total variation.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Brain / diagnostic imaging*
  • Humans
  • Image Processing, Computer-Assisted / methods*
  • Magnetic Resonance Imaging / methods*
  • Neuroimaging / methods*