Stable determination of surface impedance on a rough obstacle by far field data

TL;DR

This paper establishes a log-log stability estimate for determining the surface impedance of a Lipschitz obstacle from far-field scattering data, extending previous results that required smoother boundaries.

Contribution

It proves a new stability estimate for inverse scattering problems with less regular obstacle boundaries, specifically Lipschitz instead of C^{1,1}-smooth.

Findings

Log-log stability estimate for Lipschitz obstacles

Extension of previous smooth boundary results

Applicable to rough obstacle boundary determination

Abstract

We treat the stability of determining the boundary impedance of an obstacle by scattering data, with a single incident field. A previous result by Sincich (SIAM J. Math. Anal. 38, (2006), 434-451) showed a log stability when the boundary of the obstacle is assumed to be C^{1,1}-smooth. We prove that, when the obstacle boundary is merely Lipschitz, a log-log type stability still holds.