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Quantitative Susceptibility Mapping for MRI part 1

version (5.73 MB) by Job
Superfast Quantitative Susceptibility Mapping from MRI phase data.


Updated 28 Apr 2016

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Efficient implementation of 'Closed-form l2-Regularized QSM', proposed by B. Bilgic et al.
Here the susceptibility distribution is calculated that has an optimal balance between:
- explaining the measured field (minimal residual)
- a smooth appareance (minimal difference between neighbouring voxels)
Original Software:
B. Bilgic, I. Chatnuntawech, A.P. Fan, K. Setsompop, S.F. Cauley, L.L. Wald, E. Adalsteinsson; "Fast Image Reconstruction with L2-Regularization" Journal of Magnetic Resonance Imaging.
Please refer to this and the other two references when using this script.
Adaptations in this script:
1) Instant parameter sweep: In the original method the optimal regularization is determined by performing a series of reconstructions, from which the 'best reconstruction' is selected afterwards (L-curve sweeping). Here the calculation of this optimal parameter is reduced more than twentyfold, by rewriting the needed calculations. Even when the optimal parameter is chosen on forehand, this enables to validate this chosen regularization weight for each reconstruction just in a second.
2) Automatic wrap around prevention: Fourier-related streaks are automatically eliminated using a 'virtual buffer'. This exempts the user from adding a sufficient spatial buffer to prevent wrap-around streaking. This principle is described in: "Job G. Bouwman, Chris J.G. Bakker. Alias subtraction more efficient than conventional zero-padding in the Fourier-based calculation of the susceptibility induced perturbation of the magnetic field in MR. 2012, Magnetic Resonance in Medicine 68:621630 (2012)." Please refer to this and the other two references when using this script.

A detailed description on these adaptations is currently under review as an abstract, submitted to the ISMRM 2015: "Regularized QSM with instant parameter sweep and reduced streaking artifacts in seconds", Job G Bouwman, Peter R Seevinck. Please refer to this and the other two references when using this script.

For L1-regularized, magnitude weighted QSM, see:

Cite As

Job (2022). Quantitative Susceptibility Mapping for MRI part 1 (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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