  Artifacts in quantitative susceptibility mapping (QSM) are analyzed to
establish an optimal design criterion for QSM inversion algorithms. The
magnetic field data is decomposed into two parts, dipole compatible and
incompatible parts. The dipole compatible part generates the desired
non-streaking solution. The dipole incompatible part, including noise,
discretization error, and anisotropy sources, generates artifacts defined by a
wave propagator with the B0 field direction as the time axis. Granular noise
causes streaking and contiguous error causes both streaking and shadow
artifacts. As an example, truncation-based QSM algorithms are inherently prone
to streaking artifacts because of the deviation of the dipole kernel during
truncation. Through numerical phantom and imaging experiments, several QSM
methods, including a Bayesian regularization method and the k-space truncation
methods, were compared to show that the Bayesian approach with a structural
prior provides advantages in terms of both image quality and quantitative
measures.
