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Fast quantitative susceptibility mapping with L1‐regularization and automatic parameter selection
Author(s) -
Bilgic Berkin,
Fan Audrey P.,
Polimeni Jonathan R.,
Cauley Stephen F.,
Bianciardi Marta,
Adalsteinsson Elfar,
Wald Lawrence L.,
Setsompop Kawin
Publication year - 2014
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.25029
Subject(s) - algorithm , solver , regularization (linguistics) , computer science , smoothing , quantitative susceptibility mapping , total variation denoising , inverse problem , tikhonov regularization , nonlinear system , mathematical optimization , mathematics , artificial intelligence , computer vision , noise reduction , mathematical analysis , physics , medicine , magnetic resonance imaging , radiology , quantum mechanics
Purpose To enable fast reconstruction of quantitative susceptibility maps with total variation penalty and automatic regularization parameter selection. Methods ℓ 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. 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 ℓ 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. Magn Reson Med 72:1444–1459, 2014. © 2013 Wiley Periodicals, Inc.