Inverse obstacle scattering regularized by the tangent-point energy
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911322961084416 |
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| author | Schumacher, Henrik Rönsch, Jannik Hohage, Thorsten Wardetzky, Max |
| author_facet | Schumacher, Henrik Rönsch, Jannik Hohage, Thorsten Wardetzky, Max |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse obstacle scattering regularized by the tangent-point energy Schumacher, Henrik Rönsch, Jannik Hohage, Thorsten Wardetzky, Max Numerical Analysis Graphics Differential Geometry 65J22, 65N38 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. |
| title | Inverse obstacle scattering regularized by the tangent-point energy |
| topic | Numerical Analysis Graphics Differential Geometry 65J22, 65N38 |
| url | https://arxiv.org/abs/2512.14590 |