A direct imaging method for the exterior and interior inverse scattering problems

TL;DR

This paper introduces a direct imaging technique for reconstructing the shape of obstacles or cavities in acoustic scattering problems using boundary measurements and Fourier-Bessel functions, with proven boundary detection and numerical validation.

Contribution

It presents a novel boundary-condition-based direct imaging method for inverse acoustic scattering that accurately reconstructs shapes from boundary measurements.

Findings

The indicator functions vanish only on the boundary of the obstacle or cavity.

Numerical examples confirm the effectiveness of the proposed method.

The method accurately reconstructs shapes using boundary measurements and Fourier-Bessel functions.

Abstract

This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape of the obstacle or cavity. First, the scattered fields are approximated by the Fourier-Bessel functions with the measurements on a closed curve. Then, the indicator functions are established by the superpositions of the total fields or their derivatives to the incident point sources. We prove that the indicator functions vanish only on the boundary of the obstacle or cavity. Numerical examples are also included to demonstrate the effectiveness of the method.