A Factorization Method for Support Recovery in Magnetic Induction Tomography
Abstract
We develop a factorization framework for magnetic induction tomography in the eddy-current regime. The induced current density is represented by a divergence-free current vector potential, and the external excitation by magnetic dipole densities on an observation sphere. This choice reveals a natural physical factorization of the near-field operator into a data operator, an interior boundary response operator, and an adjoint counterpart. By introducing the Riesz map on the flux space, we recast this factorization in a Hilbert-space setting, which yields a positive-semidefinite operator with a coercive middle factor. Douglas' range theorem then identifies the range of the square root of this dissipative operator with the range of the data operator. For inclusions with a regular boundary, this range identity yields a uniqueness theorem for the support of the conductivity. This characterization leads to a non-iterative spectral indicator based on a regularized Picard quotient computed from the Hermitian imaginary part of the near-field data matrix. The reconstruction stage requires no forward solves. Numerical experiments confirm that the indicator localizes and separates the inclusions accurately, degrades gracefully under increasing noise, and captures non-convex support geometry without any convexity prior.
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BibTeX
@misc{chen2026factorization,
title = {{A Factorization Method for Support Recovery in Magnetic Induction Tomography}},
author = {Junqing Chen and Chengzhe Jiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18235},
eprint = {2609.18235},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18235},
}
RIS
TY - UNPB
TI - A Factorization Method for Support Recovery in Magnetic Induction Tomography
AU - Junqing Chen
AU - Chengzhe Jiang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18235
UR - https://arxiv.org/abs/2609.18235
AB - We develop a factorization framework for magnetic induction tomography in the eddy-current regime. The induced current density is represented by a divergence-free current vector potential, and the external excitation by magnetic dipole densities on an observation sphere. This choice reveals a natural physical factorization of the near-field operator into a data operator, an interior boundary response operator, and an adjoint counterpart. By introducing the Riesz map on the flux space, we recast this factorization in a Hilbert-space setting, which yields a positive-semidefinite operator with a coercive middle factor. Douglas' range theorem then identifies the range of the square root of this dissipative operator with the range of the data operator. For inclusions with a regular boundary, this range identity yields a uniqueness theorem for the support of the conductivity. This characterization leads to a non-iterative spectral indicator based on a regularized Picard quotient computed from the Hermitian imaginary part of the near-field data matrix. The reconstruction stage requires no forward solves. Numerical experiments confirm that the indicator localizes and separates the inclusions accurately, degrades gracefully under increasing noise, and captures non-convex support geometry without any convexity prior.
ER -