Module chi_sep_medi 

Chi-separation using MEDI-based coupled optimization

Separates total susceptibility into paramagnetic (chi+) and diamagnetic (chi-) components using chi_pos + chi_neg formulation: chi_pos >= 0 (paramagnetic, iron), in Hz internally chi_neg <= 0 (diamagnetic, myelin), in Hz internally chi_total = chi_pos + chi_neg

Forward model (all in Hz): field = D * (chi_pos + chi_neg) R2’(Hz) = dr_p_eff * chi_pos + dr_q_eff * (-chi_neg) = dr_p_eff * |chi_pos| + dr_q_eff * |chi_neg| where dr_eff = ppm_factor * Dr (dimensionless effective relaxivity)

The constraints (chi_pos >= 0, chi_neg <= 0) naturally break the gauge freedom of the chi_pos + chi_neg formulation. In most voxels, either chi_pos = 0 or chi_neg = 0, which pins one variable to its constraint boundary and prevents correlated drift.

Reference: Shin, H., et al. (2021). “chi-separation: Magnetic susceptibility source separation toward iron and myelin mapping in the brain.” NeuroImage, 240:118371.

Structs

ChiSepWorkspace 🔒

Workspace for chi-separation — holds all reusable buffers (f32).

Functions

apply_chisep_operator 🔒

Apply chi-sep Hessian operator A to doubled vector dx = [d_pos; d_neg].

cg_solve_chisep 🔒

CG solver for the doubled chi-sep system.

chi_sep_medi

Chi-separation using MEDI-based coupled optimization.

chi_sep_medi_with_progress

Chi-separation with progress callback.