Structure Prior Effects in Bayesian Approaches of Quantitative Susceptibility Mapping

Abstract

Quantitative susceptibility mapping (QSM) has shown its potential for anatomical and functional MRI, as it can quantify, for in vivo tissues, magnetic biomarkers and contrast agents which have differential susceptibilities to the surroundings substances. For reconstructing the QSM with a single orientation, various methods have been proposed to identify a unique solution for the susceptibility map. Bayesian QSM approach is the major type which uses various regularization terms, such as a piece-wise constant, a smooth, a sparse, or a morphological prior. Six QSM algorithms with or without structure prior are systematically discussed to address the structure prior effects. The methods are evaluated using simulations, phantom experiments with the given susceptibility, and human brain data. The accuracy and image quality of QSM were increased when using structure prior in the simulation and phantom compared to same regularization term without it, respectively. The image quality of QSM method using the structure prior is better comparing, respectively, to the method without it by either sharpening the image or reducing streaking artifacts in vivo. The structure priors improve the performance of the various QSMs using regularized minimization including L1, L2, and TV norm.

Quantitative Susceptibility Mapping (QSM) Algorithms: Mathematical Rationale and Computational Implementations

“…These edge indicators are derived from the magnitude image associated with the unknown susceptibility map under the assumption that edges in the two images coexist. Therefore, the weighted anisotropic total variation Ω |M∇χ| 1 penalizes only the regions where tissue structure is not expected [93].…”

“…Incorporating tissue edge information into TV is a notable feature of MEDI [93]. Recall that streaking and tissue boundaries have similar penalties in terms of TV, but streaking only appears along the singular support of the double-cone Υ, making it distinct from the tissue edges.…”

A robust multi-scale approach to quantitative susceptibility mapping

“…by spatially weighting the regulariser). Such priors help condition an otherwise ill-posed inversion operation ( Kee et al., 2017 ; Wang et al., 2013 , 2016 ).…”

“…Beyond the action range of variational regularisers, some previously proposed (inversion-only) algorithms have shown relative success in controlling reconstruction artefacts. For example, the nonlinear Morphology-Enabled Dipole Inversion (nMEDI) approach ( Liu et al., 2013 ) capitalises on the following additional strategies: (i) it incorporates a nonlinear consistency term to improve noise management, (ii) it dynamically rejects cost contributions from potentially inconsistent data (to prevent them from dominating the data-fidelity weight), and (iii) it promotes piece-wise constant susceptibility distributions except at locations of strong 3D magnitude gradient, which reduces streaking artefacts and helps better resolve the vasculature and other local features ( Kee et al., 2017 ; Liu et al., 2011 , 2012a ; Wang et al., 2016 ).…”

Coherence enhancement in quantitative susceptibility mapping by means of anisotropic weighting in morphology enabled dipole inversion

“…The idea of using isotropic binary weights in total variation was proposed in in the context of Bayesian QSM. It has been subsequently shown in that using binary weights derived from the magnitude image (structural consistency priors) improves the performance of QSM compared with unweighted (standard) total variation in QSM. As mentioned in the Introduction, these binary weights were also used as spatial priors in , demonstrating its promising performance in QSM.…”