Inverse obstacle scattering regularized by the tangent-point energy
Abstract
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.
Fields of Study & Subjects
Numerical methods in inverse problems
Microwave Imaging and Scattering Analysis
Sparse and Compressive Sensing Techniques
Publication details
- Journal / source
- Inverse Problems
- Publisher
- IOP Publishing
- Volume
- 42
- Issue
- 9
- Pages
- 095002–095002
- Publication date
- 3 August 2026
- Language
- EN