Author(s)

A. Karageorghis & D. Lesnic

Abstract

In this paper we propose a simple method for detecting (shape, size and location) a scatterer embedded in a host acoustic homogeneous medium from scant measurements of the scattered acoustic pressure in the vicinity (near-or far-field) of the obstacle. We develop a nonlinear constrained minimization regularized method of fundamental solutions for obtaining the numerical solution of the inverse problem. The stability of the numerical scheme is investigated by inverting measurements contaminated with noise. Keywords: inverse acoustic scattering, method of fundamental solutions. 1 Introduction The inverse problems of time-harmonic acoustic scattering of waves from obstacles of arbitrary shape embedded in a fluid, or solid medium have been of considerable interest to researchers for many years, see e.g. [1]. In addition to being of academic interest, these problems have physical applications in the fields of radar and sonar detection; the ability to \“see” in real time in complete darkness in murky water for deep sea submarines, underwater surveillance and target acquisition, detection of objects in the ocean, either fully submerged or partially buried in the seafloor, ultrasound medical imaging of soft tissues, nondestructive testing of materials, etc. The inverse problem we consider in this paper is to determine the boundary of an insonified scatterer from scant measurements of its response when excited by impinging plane waves. The scatterer can be sound-soft, sound-hard or convectively embedded in the full-space. Although some uniqueness results are known, notably in [2], the problem is still difficult to solve since it is nonlinear,

Keywords

inverse acoustic scattering, method of fundamental solutions