Expand description
Weak-Harmonic QSM (WH-QSM) dipole inversion
Jointly estimates the susceptibility map x AND a residual harmonic
background field phi_h, so that any harmonic (Laplacian-null) field
remaining after background-field removal is absorbed into phi_h instead
of corrupting the susceptibility estimate. This makes the reconstruction
robust to imperfect background-field removal.
The optimization solves a nonlinear total-variation problem via ADMM,
with an additional weak-harmonic regularization term coupling x and the
harmonic field. The data-fidelity term is nonlinear (sine of the phase),
and is solved with an inner Newton iteration.
Reference: Milovic, C., Bilgic, B., Zhao, B., Acosta-Cabronero, J., Tejos, C. (2019). “Weak-harmonic regularization for quantitative susceptibility mapping.” Magnetic Resonance in Medicine, 81(2):1399-1411. https://doi.org/10.1002/mrm.27483
Ported from FANSI’s WH_nlTV.m.
§Units / phase_scale
The nonlinear data term operates on a wrapped phase. The input
local_field is multiplied by params.phase_scale to form the internal
phase, and the final susceptibility map is divided by phase_scale. For
field data already in ppm-consistent units (as the rest of QSM.rs assumes),
use phase_scale = 1.0. When the input is a raw radians phase and a
ppm-scaled output is desired, set phase_scale to the radians→ppm factor.
Structs§
- WhQsm
Params - WH-QSM parameters.