Stability estimates for an inverse scattering problem at high frequencies

TL;DR

This paper establishes Lipschitz stability for low-frequency potential recovery and demonstrates the possibility of infinite resolution in near-field inverse scattering at high frequencies for radial potentials near the boundary.

Contribution

It provides new stability estimates for inverse scattering problems at high frequencies and shows infinite resolution is achievable under specific conditions.

Findings

Lipschitz stability for low-frequency potential components

Infinite resolution possible for radial potentials near the boundary

High-frequency measurements enable detailed potential reconstruction

Abstract

We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that, in the case of a radial potential supported sufficiently near the boundary, infinite resolution can be achieved from measurements of the near-field operator in the monotone case.