A Sparsity-Promoting Electromagnetic Inversion Method Regularized by ℓ1 / ℓ2-Norm of the Model Gradient
Abstract
A nonlinear EM inversion method regularized by ℓ1 / ℓ2-norm of the model gradient is proposed. The ℓ1 / ℓ2-norm, defined as the ratio of ℓ1-norm to ℓ2-norm, exhibits a scale-invariant property that enables it to more accurately characterize sparsity in the solution compared with the conventional ℓ1-norm. To address the nonconvexity and nonsmoothness introduced by the quotient structure of ℓ1 / ℓ2-norm, the inversion problem is reformulated and solved using the alternating direction method of multipliers, resulting in an efficient optimization algorithm comprising five sub-steps. The Gauss--Newton method is incorporated into the first sub-step to linearize the nonlinear inversion. The proposed method is validated by a series of numerical examples using both synthetic and experimental datasets, and is compared against standard regularization methods such as Tikhonov and total variation. The results demonstrate that the proposed method yields superior reconstructions of permittivity profiles, particularly in preserving sharp edges and suppressing artifacts, without incurring additional computational cost. Furthermore, the method exhibits strong robustness to measurement noise and reduced sensitivity to the choice of the regularization weight.
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BibTeX
@misc{gao2026sparsitypromoting,
title = {{A Sparsity-Promoting Electromagnetic Inversion Method Regularized by $\ell_1 / \ell_2$-Norm of the Model Gradient}},
author = {Lingqi Gao and Hakan Bagci},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06524},
eprint = {2609.06524},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06524},
}
RIS
TY - UNPB
TI - A Sparsity-Promoting Electromagnetic Inversion Method Regularized by ℓ_1 / ℓ_2-Norm of the Model Gradient
AU - Lingqi Gao
AU - Hakan Bagci
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06524
UR - https://arxiv.org/abs/2609.06524
AB - A nonlinear EM inversion method regularized by ℓ_1 / ℓ_2-norm of the model gradient is proposed. The ℓ_1 / ℓ_2-norm, defined as the ratio of ℓ_1-norm to ℓ_2-norm, exhibits a scale-invariant property that enables it to more accurately characterize sparsity in the solution compared with the conventional ℓ_1-norm. To address the nonconvexity and nonsmoothness introduced by the quotient structure of ℓ_1 / ℓ_2-norm, the inversion problem is reformulated and solved using the alternating direction method of multipliers, resulting in an efficient optimization algorithm comprising five sub-steps. The Gauss--Newton method is incorporated into the first sub-step to linearize the nonlinear inversion. The proposed method is validated by a series of numerical examples using both synthetic and experimental datasets, and is compared against standard regularization methods such as Tikhonov and total variation. The results demonstrate that the proposed method yields superior reconstructions of permittivity profiles, particularly in preserving sharp edges and suppressing artifacts, without incurring additional computational cost. Furthermore, the method exhibits strong robustness to measurement noise and reduced sensitivity to the choice of the regularization weight.
ER -