The inverse obstacle scattering with incident tapered waves

TL;DR

This paper introduces a direct imaging method using narrow tapered waves for reconstructing obstacle shapes in acoustic scattering, offering local illumination, high resolution, and computational efficiency.

Contribution

It presents a novel approach utilizing tapered waves for inverse obstacle scattering, enhancing local imaging and resolution over traditional methods.

Findings

Tapered waves improve local boundary reconstruction.

The imaging scheme is mathematically stable.

Numerical examples confirm effectiveness of tapered waves.

Abstract

This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging algorithm. The stability of the imaging scheme is mathematically analyzed. We emphasize that different from the incident plane waves or point sources, the tapered waves with narrow widths bring several benefits in the inverse scattering: 1. local property. A tapered wave can illuminate only on a local part of the boundary of the obstacle, which generates the scattered field; 2. high resolution. We need only reconstruct the boundary near the beam, which improves the quality of some well-known algorithms; 3. fast and easy to implement. Numerical examples are included to demonstrate the effectiveness of the tapered waves.