Module tfi 

TFI (Preconditioned Total Field Inversion)

Single-step QSM: inverts the TOTAL field (before background removal) directly to susceptibility over the whole field-of-view, jointly handling background removal and dipole inversion.

It reuses MEDI’s nonlinear Gauss-Newton + CG + IRLS(L1) machinery, with three differences from MEDI (local-field inversion):

1. Input is the total field (not background-removed), solved over the whole FOV (not just the brain mask).
2. A preconditioner change-of-variables χ = P⊙y is used, where P[i] = 1 inside the brain mask and P[i] = precond (default 30) outside. Solving for y is better conditioned because background susceptibility (e.g. air ≈ 9 ppm) is far larger than tissue. With χ = P⊙y the Gauss-Newton normal equation operator on δy is A_tfi(δy) = P ⊙ A_medi(P ⊙ δy) and the RHS is b_tfi = P ⊙ b_medi(χ = P⊙y).
3. Regularization (L1 morphology) is applied over the whole FOV: the magnitude edge mask is used inside the brain and set to 1 (regularize) OUTSIDE the brain. The data-fidelity weight is SNR/brain-based (≈0 outside the brain), so outside-brain χ is constrained by regularization + the preconditioner.

Reference: Liu, Z., Kee, Y., Zhou, D., Wang, Y., Spincemaille, P. (2017). “Preconditioned total field inversion (TFI) algorithm for quantitative susceptibility mapping.” Magnetic Resonance in Medicine, 78(1):303-315. https://doi.org/10.1002/mrm.26946

Structs

TfiParams

TFI algorithm parameters

Functions

cg_solve_tfi 🔒

Conjugate gradient solver for the preconditioned TFI operator.

tfi

Preconditioned Total Field Inversion (TFI).