We provide a mathematical understanding for artifacts in QSM, particularly streaking artifacts. 1) The local field data can be decomposed into a dipole-compatible part and a dipole-incompatible part. 2) In spatially continuous space, the streaking-free susceptibility solution is obtained from the dipole-compatible field data only, and the dipole-incompatible data leads to artifacts defined by a wave propagator with z as time, specifically, streaking artifacts from granular noise and shadow artifacts from white matter noise error. Although it is not known how to filter out such dipole-incompatible data, its artifacts can be suppressed in regularization-based Bayesian methods such as MEDI, which can efficiently penalize streaking artifacts. k-space-truncation-based methods that generate additional dipole-incompatible data near the zero cone amplify streaking artifacts.
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