Inverse obstacle scattering regularized by the tangent-point energy

Henrik Schumacher; Jannik Rönsch; Thorsten Hohage; Max Wardetzky

doi:10.1088/1361-6420/ae9439

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arXiv · 2512.14590

Inverse obstacle scattering regularized by the tangent-point energy

Henrik Schumacher·Jannik Rönsch·Thorsten Hohage·Max Wardetzky

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Abstract

We employ the so-called tangent-point energy as Tikhonov regularizer for ill-conditioned inverse scattering problems in 3D. The tangent-point energy is a self-avoiding functional on the space of embedded surfaces that also penalizes surface roughness. Moreover, it features nice compactness and continuity properties. These allow us to show the well-posedness of the regularized problems and the convergence of the regularized solutions to the true solution in the limit of vanishing noise level. We also provide a reconstruction algorithm of iteratively regularized Gauss-Newton type. Our numerical experiments demonstrate that our method is numerically feasible and effective in producing reconstructions of unprecedented quality.

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Henrik Schumacher, Jannik Rönsch, Thorsten Hohage, Max Wardetzky. 2026-09-08. Inverse obstacle scattering regularized by the tangent-point energy. https://doi.org/10.1088/1361-6420/ae9439

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