Weak-harmonic regularization for quantitative susceptibility mapping.

Area of Science:

• Medical Imaging
• Biophysics
• Computational Science

Background:

• Quantitative susceptibility mapping (QSM) requires background-field removal, a step prone to residual errors.
• These errors contaminate local field estimations, leading to inaccurate tissue susceptibility reconstructions.

Purpose of the Study:

• To develop a novel approach for QSM that simultaneously separates background field contributions and local susceptibility sources.
• To mitigate artifacts caused by residual background fields in QSM.

Main Methods:

• Developed a weak-harmonic regularizer to constrain and separate background field components from local effects in QSM phase data.
• Employed the alternating directions of multipliers method (ADMM) for efficient optimization and fast convergence.
• Introduced an ADMM-based preconditioned nonlinear projection onto dipole fields solver for improved initialization with wrapped-phase data.

Main Results:

• Weak-harmonic QSM demonstrated improved reconstruction quality compared to the standard total variation QSM algorithm.
• Artifacts such as streaking and shadowing were significantly suppressed.
• Residual background components were effectively removed, leading to more accurate susceptibility maps.

Conclusions:

• Weak-harmonic QSM, particularly with field preconditioning, is a robust dipole inversion technique.
• This method shows potential for extension into a single-step formulation for processing uncombined multi-echo data.