Solving an inverse obstacle problem for the wave equation by using the boundary control method

TL;DR

This paper extends a boundary control method to locate sound hard obstacles in any dimension using wave equation measurements, demonstrating robustness through numerical experiments with noisy data.

Contribution

The paper generalizes a previous method to higher dimensions for identifying sound hard obstacles from boundary measurements.

Findings

Method successfully locates obstacles in simulated noisy data

Robustness against measurement noise demonstrated

Extension from wave speed discontinuities to sound hard obstacles

Abstract

We introduced in [arXiv:1106.3204] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic Neumann-to-Dirichlet operator. Here we extend the method for sound hard obstacles in arbitrary dimension. We present numerical experiments with simulated noisy data suggesting that the method is robust against measurement noise.