Inverse obstacle scattering regularized by the tangent-point energy

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.