Computed Inverse Resonance Imaging for Magnetic Susceptibility Map Reconstruction

Chen, Zikuan; Calhoun, Vince D.

doi:10.1097/rct.0b013e3182455cab

Cited by 29 publications

(79 citation statements)

References 25 publications

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“…These include truncation for k-space division [13,34,39,42,49], weighted k-space derivatives [20], piecewise constant susceptibility [6,33], smooth susceptibility or susceptibility gradients [17], sparse susceptibility gradients or wavelets [1,2,3,17,50], and morphological consistency of the susceptibility map [7,17,21,35]. The search for the best prior is ongoing.…”

Section: Discussionmentioning

confidence: 99%

Inverse Problem in Quantitative Susceptibility Mapping

Choi¹,

Park²,

Wang³

et al. 2014

SIAM J. Imaging Sci.

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Quantitative susceptibility mapping (QSM) is a new medical imaging technique that can visualize magnetic susceptibility, changes of which in tissue indicate various disease processes involving iron transport. The inverse problem of QSM is to recover the susceptibility distribution of the human body from the measured local field that is expressed by the convolution of the susceptibility distribution with the magnetic field generated by a unit dipole. The inverse problem is ill-posed due to the presence of zeros at a cone in the Fourier representation of the unit dipole kernel. Reconstruction methods have been greatly improved to give better recovery of tissue susceptibility data for QSM, and various clinical applications have been pursued. However, rigorous mathematical analyses for the inverse problem, such as demonstrations of the existence and uniqueness of solutions and error characterizations, have not yet been presented. This paper provides for the first time not only a theoretical ground for QSM but also the underlying cause of streaking artifacts.

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Section: Discussionmentioning

confidence: 99%

Inverse Problem in Quantitative Susceptibility Mapping

Choi¹,

Park²,

Wang³

et al. 2014

SIAM J. Imaging Sci.

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“…These are also known as split‐Bregman iterations and have been deployed successfully in compressed sensing applications for MRI . A variable‐splitting method for susceptibility mapping similar to the proposed algorithm was proposed in , which aims to solve

m i n_{χ, y, v} \frac{1}{2} | | v - {boldnormalF}^{- 1} D F χ - z_{t} | |_{2}^{2} + λ \cdot | | y | |_{1} + \frac{μ}{2} | | y - G χ - η_{t} | |_{2}^{2} + \frac{γ}{2} | | v ‐ ϕ | |_{2}^{2}

Compared with our formulation in Equation , this introduces a new variable v and a third regularization parameter γ. Because the tissue phase ϕ is the observed data, it should not be necessary to further introduce an auxiliary variable v to penalize these observations.…”

Section: Discussionmentioning

confidence: 99%

“…Combined with state‐of‐the‐art phase unwrapping and background phase removal methods , this comprised a fast reconstruction pipeline that might facilitate clinical application of QSM. In the Discussion section, we outline the differences between the presented methods and a similar variable‐splitting algorithm for QSM previously proposed in the elegant contribution by Chen and Calhoun .…”

Section: Introductionmentioning

confidence: 99%

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

Bilgic̦

Fan

Polimeni

et al. 2013

Magnetic Resonance in Med

115

137

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Purpose To enable fast reconstruction of quantitative susceptibility maps with Total Variation penalty and automatic regularization parameter selection. Methods ℓ1-regularized susceptibility mapping is accelerated by variable-splitting, which allows closed-form evaluation of each iteration of the algorithm by soft thresholding and FFTs. 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 to the nonlinear Conjugate Gradient (CG) solver, the proposed method offers 20× speed-up in reconstruction time. A complete pipeline including Laplacian phase unwrapping, background phase removal with SHARP filtering and ℓ1-regularized dipole inversion at 0.6 mm isotropic resolution is completed in 1.2 minutes using Matlab on a standard workstation compared to 22 minutes using the Conjugate Gradient solver. This fast reconstruction allows estimation of regularization parameters with the L-curve method in 13 minutes, which would have taken 4 hours with the CG algorithm. 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× faster than the nonlinear CG approach. Utility of the proposed method is also demonstrated in functional BOLD 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.

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“…Susceptibility is relevant to the main magnetic field, B 0 , of a magnetic resonance imaging (MRI) system. The field of the induced magnetization can be measured using MRI signal phases and can be deconvolved to yield quantitative susceptibility maps (QSMs) [1-9]. QSMs provide a noninvasive means of assessing iron deposition [5,8,10-17], blood oxygen saturation [6,10,18,19], the myelin in white matter tracts [7,20,21], cortical and deep gray matter structures and substructures [17,22-25], and the biodistribution of contrast agents for clinical and preclinical investigations [26,27].…”

Section: Introductionmentioning

confidence: 99%

Phase-corrected bipolar gradients in multi-echo gradient-echo sequences for quantitative susceptibility mapping

Chang

Lan³

et al. 2014

Magn Reson Mater Phy

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Object The large echo spacing of unipolar readout gradients in current multiecho gradient-echo sequences for mapping fields in quantitative susceptibility mapping (QSM) can be reduced using bipolar readout gradients to improve acquisition efficiency. Materials and Methods Phase discrepancies between odd and even echoes in the bipolar readout gradients caused by non-ideal gradient behaviors were measured, modeled as polynomials in space and corrected for accordingly in field mapping. The bipolar approach for multiecho gradient-echo field mapping was compared with the unipolar approach for QSM. Results The odd-even-echo phase discrepancies were approximately constant along the phase encoding direction and linear along the readout and slice-selection directions. A simple linear phase correction in all three spatial directions was shown to enable accurate QSM in the human brain using a bipolar multiecho GRE sequence. Bipolar multiecho acquisition provides QSM in good quantitative agreement with unipolar acquisition while also reducing noise. Conclusion With a linear phase correction between odd-even echoes, bipolar readout gradients can be used in multiecho gradient-echo sequences for QSM.

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Computed Inverse Resonance Imaging for Magnetic Susceptibility Map Reconstruction

Cited by 29 publications

References 25 publications

Inverse Problem in Quantitative Susceptibility Mapping

Inverse Problem in Quantitative Susceptibility Mapping

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

Phase-corrected bipolar gradients in multi-echo gradient-echo sequences for quantitative susceptibility mapping

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