2025/12/16 by Schumacher, Henrik, Rönsch, Jannik, Hohage, Thorsten +1
#65J22 #65N38 #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2512.14590
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.