Inverse Problem in Quantitative Susceptibility Mapping

Choi, Jae Kyu; Park, Hyoung Suk; Wang, Shuai; Wang, Yi; Seo, Jin Keun

doi:10.1137/140957433

Cited by 31 publications

(58 citation statements)

References 40 publications

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“…Several recently proposed methods similarly circumvent background field removal to estimate susceptibility directly from the total field . These methods are based on the partial differential formulation of the signal equation (Eq. []):

Δ f = Δ (d * (χ_{B} + χ_{L})) = (\frac{1}{3} Δ - \frac{\partial^{2}}{\partial z^{2}}) χ_{L} .

…”

Section: Theorymentioning

confidence: 99%

Preconditioned total field inversion (TFI) method for quantitative susceptibility mapping

Liu

Kee

Zhou

et al. 2016

Magnetic Resonance in Med

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112

169

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Purpose To investigate systematic errors in traditional quantitative susceptibility mapping (QSM) where background field removal and local field inversion (LFI) are performed sequentially, to develop a total field inversion (TFI) QSM method to reduce these errors, and to improve QSM quality in the presence of large susceptibility differences. Theory and Methods The proposed TFI is a single optimization problem which simultaneously estimates the background and local fields, preventing error propagation from background field removal to QSM. To increase the computational speed, a new preconditioner is introduced and analyzed. TFI is compared with the traditional combination of background field removal and LFI in a numerical simulation and in phantom, 5 healthy subjects and 18 patients with intracerebral hemorrhage. Results Compared with the traditional method PDF+LFI, preconditioned TFI substantially reduced error in QSM along the air-tissue boundaries in simulation, generated high-quality in vivo QSM within similar processing time, and suppressed streaking artifacts in intracerebral hemorrhage QSM. Moreover, preconditioned TFI was capable of generating QSM for the entire head including the brain, air-filled sinus, skull, and fat. Conclusion Preconditioned total field inversion improves the accuracy of QSM over the traditional method where background and local fields are separately estimated.

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Δ f = Δ (d * (χ_{B} + χ_{L})) = (\frac{1}{3} Δ - \frac{\partial^{2}}{\partial z^{2}}) χ_{L} .

…”

Section: Theorymentioning

confidence: 99%

Preconditioned total field inversion (TFI) method for quantitative susceptibility mapping

Liu

Kee

Zhou

et al. 2016

Magnetic Resonance in Med

Self Cite

112

169

View full text Add to dashboard Cite

show abstract

“…There are other solvers available including interior point methods or split Bregman method [36]. The reconstructed QSM image may be affected by the solver used in a given algorithm.…”

Section: Discussionmentioning

confidence: 99%

Structure Prior Effects in Bayesian Approaches of Quantitative Susceptibility Mapping

Wang

Chen

Wang

et al. 2016

BioMed Research International

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Quantitative susceptibility mapping (QSM) has shown its potential for anatomical and functional MRI, as it can quantify, for in vivo tissues, magnetic biomarkers and contrast agents which have differential susceptibilities to the surroundings substances. For reconstructing the QSM with a single orientation, various methods have been proposed to identify a unique solution for the susceptibility map. Bayesian QSM approach is the major type which uses various regularization terms, such as a piece-wise constant, a smooth, a sparse, or a morphological prior. Six QSM algorithms with or without structure prior are systematically discussed to address the structure prior effects. The methods are evaluated using simulations, phantom experiments with the given susceptibility, and human brain data. The accuracy and image quality of QSM were increased when using structure prior in the simulation and phantom compared to same regularization term without it, respectively. The image quality of QSM method using the structure prior is better comparing, respectively, to the method without it by either sharpening the image or reducing streaking artifacts in vivo. The structure priors improve the performance of the various QSMs using regularized minimization including L1, L2, and TV norm.

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“…The gradient echo (GRE) sequence is commonly used to acquire complex data sensitive to tissue magnetic susceptibility

χ (bold-italicr)

, where

r = (x, y, z) \in ℝ^{3}

is a position vector. The

z

‐component (along the

B_{0}

direction) of the magnetic field generated by tissue and experienced by a water proton,

b (bold-italicr)

(measured in the unit of

B_{0}

), can then be estimated from the GRE complex data using phase unwrapping and background field removal; this is modeled according to Maxwell's equations for static magnetism as

b (bold-italicr) = (d * χ) (bold-italicr) .

…”

Section: Theorymentioning

confidence: 99%

Coherence enhancement in quantitative susceptibility mapping by means of anisotropic weighting in morphology enabled dipole inversion

Kee

Cho

Deh

et al. 2017

Magnetic Resonance in Med

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Inverse Problem in Quantitative Susceptibility Mapping

Cited by 31 publications

References 40 publications

Preconditioned total field inversion (TFI) method for quantitative susceptibility mapping

Preconditioned total field inversion (TFI) method for quantitative susceptibility mapping

Structure Prior Effects in Bayesian Approaches of Quantitative Susceptibility Mapping

Coherence enhancement in quantitative susceptibility mapping by means of anisotropic weighting in morphology enabled dipole inversion

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