A linear sampling method for inverse acoustic scattering by a locally rough interface

TL;DR

This paper introduces a new linear sampling method for efficiently reconstructing local perturbations of a rough interface in inverse acoustic scattering problems using near-field measurements.

Contribution

A novel linear sampling approach tailored for local interface perturbations, utilizing a reformulated integral equation for fast and accurate imaging.

Findings

Effective reconstruction of interface perturbations demonstrated

Numerical experiments confirm method's accuracy and efficiency

Applicable to unbounded, locally rough surfaces

Abstract

This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local perturbation of the interface from the near-field measurement given on a straight line segment with a finite distance above the interface and generated by point sources. Precisely, we propose a novel version of the linear sampling method to recover the location and shape of the local perturbation of the interface numerically. Our method is based on a modified near-field operator equation associated with a special rough surface, constructed by reformulating the forward scattering problem into an equivalent integral equation formulation in a bounded domain, leading to a fast imaging algorithm. Numerical experiments are presented to illustrate the effectiveness of the imaging method.