Inverse obstacle scattering regularized by the tangent-point energy

TL;DR

This paper introduces a novel regularization method using tangent-point energy for 3D inverse obstacle scattering, improving solution stability and reconstruction quality.

Contribution

It proposes using tangent-point energy as a regularizer, establishing well-posedness and convergence, and develops an iterative reconstruction algorithm.

Findings

Method achieves high-quality reconstructions.

Numerical experiments confirm feasibility and effectiveness.

Provides theoretical guarantees for regularized solutions.

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.