Fast quantitative susceptibility mapping with L1-regularization and automatic parameter selection

Berkin Bilgic, Audrey P. Fan, Jonathan R. Polimeni, Stephen F. Cauley, Marta Bianciardi, Elfar Adalsteinsson, Lawrence L. Wald, Kawin Setsompop

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


Results: Compared with the nonlinear conjugate gradient (CG) solver, the proposed method is 20 times faster. A complete pipeline including Laplacian phase unwrapping, background phase removal with SHARP filtering, and '1-regularized dipole inversion at 0.6 mm isotropic resolution is completed in 1.2 min using MATLAB on a standard workstation compared with 22 min using the CG solver. This fast reconstruction allows estimation of regularization parameters with the L-curve method in 13 min, which would have taken 4 h with the CG algorithm. The proposed method also permits magnitude-weighted regularization, which prevents smoothing across edges identified on the magnitude signal. This more complicated optimization problem is solved 5 times faster than the nonlinear CG approach. Utility of the proposed method is also demonstrated in functional blood oxygen level-dependent susceptibility mapping, where processing of the massive time series dataset would otherwise be prohibitive with the CG solver.

Conclusion: Online reconstruction of regularized susceptibility maps may become feasible with the proposed dipole inversion.

Purpose: To enable fast reconstruction of quantitative susceptibility maps with total variation penalty and automatic regularization parameter selection.

Methods: '1-Regularized susceptibility mapping is accelerated by variable splitting, which allows closed-form evaluation of each iteration of the algorithm by soft thresholding and fast Fourier transforms. This fast algorithm also renders automatic regularization parameter estimation practical. A weighting mask derived from the magnitude signal can be incorporated to allow edge-aware regularization.

Original languageEnglish (US)
Pages (from-to)1444-1459
Number of pages16
JournalMagnetic Resonance in Medicine
Issue number5
StatePublished - Nov 1 2014
Externally publishedYes

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging


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