Robust and efficient MRI phase processing for magnetic susceptibility mapping

Abstract:

Quantitative susceptibility mapping (QSM) estimates tissue magnetic susceptibility from gradient-echo MRI phase measurements, providing contrast sensitive to iron, myelin, calcium, and other tissue properties. Its reconstruction is challenging because susceptibility produces a nonlocal dipole field, while measured phase is affected by wrapping, background fields, noise, acquisition choices, and reconstruction artifacts. Accurate QSM therefore depends on robust phase processing and inversion methods that address the ill-conditioned relationship between susceptibility sources and the measured phase.

This thesis develops computational methods to improve the accuracy, robustness, and efficiency of susceptibility-based MRI reconstruction. 

First, a rapid two-step dipole inversion method is proposed for single-orientation QSM. The method separates the inversion into well-conditioned and ill-conditioned components, using early-terminated Krylov iterations for the former and sparsity-regularized recovery for the latter. This provides high-quality susceptibility estimates without anatomical priors and with substantially reduced computation time.

Second, a direct multi-echo dipole inversion formulation is developed that models echo-dependent phase data as observations of a common susceptibility distribution, rather than first estimating an intermediate field map. This approach uses the acquired data more directly and is combined with a supplemental refinement strategy that reduces regularization-induced susceptibility underestimation.

Third, a parallel quality-guided minimum-spanning-tree algorithm is introduced for phase unwrapping in two and three dimensions. The method preserves path-following unwrapping behaviour while achieving large CPU and GPU speedups, including sub-second GPU unwrapping of gigabyte-scale in-vivo datasets.

Fourth, a method for unwrapping undersampled, highly aliased phase by incorporating the dipole field model into a weighted $L_p$-norm phase-unwrapping formulation is presented. By using the nonlocal structure of susceptibility-induced fields as a physical constraint, this approach enables recovery in the presence of multi-cycle aliasing.

Finally, susceptibility reconstruction from clinically available susceptibility-weighted imaging data, where stored phase is often filtered and not directly quantitative, is addressed. A learning-based phase-recovery approach is developed to recover susceptibility-relevant phase, enabling QSM when conventional reconstruction inputs are unavailable.