Sparse magnetization vector inversion with magnitude and direction constraints in Cartesian coordinates

Magnetization vector inversion (MVI) is an effective method for obtaining the magnitude and direction distributions of magnetization simultaneously without prior knowledge of magnetization directions. Nevertheless, reliable outcomes using MVI remain a challenge. This study proposes a tightly constrained MVI approach that applies the Lp norm to the magnitude and direction of magnetization to produce sparse results with uniform magnetization directions. All calculations are performed in Cartesian coordinates to preserve the linear forward operator, making calculations simple and stable. Synthetic tests demonstrate that this constrained method improves accuracy by producing models with stable magnetization directions and simple structures.