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Primal-dual and forward gradient implementation for quantitative susceptibility mapping.

Youngwook Kee1, Kofi Deh2, Alexey Dimov3

  • 1Department of Radiology, Weill Cornell Medical College, New York, New York, USA.

Magnetic Resonance in Medicine
|March 3, 2017
PubMed
Summary
This summary is machine-generated.

The primal-dual (PD) formulation offers faster convergence and improved accuracy in quantitative susceptibility mapping (QSM) compared to the Gauss-Newton conjugate gradient (GNCG) method. Using a forward difference scheme effectively reduces artifacts in QSM reconstruction.

Keywords:
Gauss-Newton conjugate gradientdiscretization methodsmorphology enabled dipole inversion (MEDI)primal-dual formulationquantitative susceptibility mapping (QSM)

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Area of Science:

  • Magnetic Resonance Imaging
  • Computational Methods in Medical Imaging

Background:

  • Quantitative susceptibility mapping (QSM) is crucial for analyzing magnetic susceptibility in biological tissues.
  • The computational efficiency and accuracy of QSM algorithms are critical for clinical applications.
  • Prior term discretization significantly impacts QSM reconstruction quality and artifact generation.

Purpose of the Study:

  • To compare the computational performance of the primal-dual (PD) formulation against the Gauss-Newton conjugate gradient (GNCG) algorithm for the prior term in QSM.
  • To evaluate the impact of central versus forward difference schemes on QSM reconstruction, specifically regarding checkerboard artifacts.

Main Methods:

  • Derived spatially continuous and PD formulations for regularized QSM inversion.
  • Implemented the Chambolle-Pock algorithm for PD and compared its convergence with GNCG.
  • Assessed forward and central difference schemes for prior term discretization on phantom and in vivo MRI data.

Main Results:

  • The PD approach demonstrated a faster convergence rate than GNCG, especially with smaller conditioning parameters.
  • Forward difference schemes effectively suppressed checkerboard artifacts compared to central difference schemes.
  • Both PD and GNCG methods showed high accuracy, validated by excellent correlation with COSMOS.

Conclusions:

  • The primal-dual formulation with a forward difference gradient scheme offers superior convergence and accuracy in QSM compared to GNCG with a central difference scheme.
  • This study highlights the importance of algorithmic choice and discretization methods for optimizing QSM reconstruction.