Fast Nonlinear Susceptibility Inversion With Variational Regularization

Abstract

Purpose: Quantitative susceptibility mapping can be performed
through the minimization of a function consisting of data
fidelity and regularization terms. For data consistency, a Gaussianphase
noise distribution is often assumed, which breaks down
when the signal-to-noise ratio is low. A previously proposed alternative
is to use a nonlinear data fidelity term, which reduces streaking
artifacts, mitigates noise amplification, and results in more accurate
susceptibility estimates. We hereby present a novel algorithm that
solves the nonlinear functional while achieving computation speeds
comparable to those for a linear formulation.
Methods: We developed a nonlinear quantitative susceptibility
mapping algorithm (fast nonlinear susceptibility inversion)
based on the variable splitting and alternating direction
method of multipliers, in which the problem is split into simpler
subproblems with closed-form solutions and a decoupled nonlinear
inversion hereby solved with a Newton-Raphson iterative
procedure. Fast nonlinear susceptibility inversion performance
was assessed using numerical phantom and in vivo experiments,
and was compared against the nonlinear morphologyenabled
dipole inversion method.
Results: Fast nonlinear susceptibility inversion achieves similar
accuracy to nonlinear morphology-enabled dipole inversion
but with significantly improved computational efficiency.
Conclusion: The proposed method enables accurate reconstructions
in a fraction of the time required by state-of-the-art
quantitative susceptibility mapping methods.