Module l1qsm 

L1-QSM: nonlinear L1 data-fidelity dipole inversion with TV regularization

Solves the nonlinear QSM inverse problem with an L1 data-fidelity term (robust to phase outliers / noise) and a total-variation prior:

min_x || W .* ( exp(i * D x) - exp(i * phi) ) ||_1 + alpha1 * ||grad(x)||_1

where D is the dipole operator, phi is the (scaled) local field phase, and W = lambda * mask. The nonlinear fidelity is linearized around the current auxiliary phase and solved with an inner complex-argument Newton iteration, all embedded in an ADMM splitting.

Reference: Milovic, C., Tejos, C., Acosta-Cabronero, J., et al. (2022). “The 2016 QSM Challenge: L1-QSM and PI-QSM — comparison of nonlinear L1 and phase-integral data-fidelity QSM reconstructions.” Magnetic Resonance in Medicine (MRM), 2022.

Ported from the FANSI toolbox nlL1TV.m (https://gitlab.com/cmilovic/FANSI-toolbox).

Structs

L1QsmParams

L1-QSM algorithm parameters.

Functions

l1qsm

L1-QSM nonlinear dipole inversion.

norm2 🔒

L2 norm of a real slice.