The enclosure method for inverse obstacle scattering over a finite time interval: V. Using time-reversal invariance

TL;DR

This paper introduces a novel enclosure method leveraging the time-reversal invariance of the wave equation to determine the minimal enclosing ball of an unknown obstacle from boundary data over finite time.

Contribution

It presents a new approach using time-reversal invariance and the lacuna phenomenon to identify the minimal enclosing ball of an obstacle from limited boundary measurements.

Findings

Successfully determines the minimal enclosing ball of the obstacle.

Utilizes the wave equation's time-reversal invariance and lacuna properties.

Operates with data from a single boundary point over finite time.

Abstract

The wave equation is time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown obstacle embedded in a known bounded domain from a single point on the graph of the so-called response operator on the boundary of the domain over a finite time interval. The occurrence of the lacuna in the solution of the free space wave equation is positively used.