The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval

TL;DR

This paper introduces a straightforward method for inverse obstacle scattering problems using finite-time wave data, enabling the determination of obstacle distances beyond the convex hull from measurements on a surrounding surface.

Contribution

The paper presents a novel enclosure method that reconstructs obstacle locations from finite-time wave measurements, extending previous approaches to more practical data collection scenarios.

Findings

Successfully determines obstacle distances from a known surface.

Applicable to wave data measured over finite time intervals.

Provides a method to go beyond convex hull limitations.

Abstract

A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is generated by an initial data with compact support outside the surface. The method yields the distance from a given point outside the surface to obstacles and thus more than the convex hull.