On finding an obstacle embedded in the rough background medium via the enclosure method in the time domain

TL;DR

This paper introduces a mathematical time-domain method for detecting obstacles within rough media using a single wave reflection, providing criteria for obstacle existence and distance estimates.

Contribution

It presents a novel enclosure method in the time domain for obstacle detection in complex backgrounds, with explicit distance bounds and practical applications.

Findings

Successfully detects obstacles using a single wave reflection.

Provides quantitative estimates of obstacle distance.

Demonstrates potential through practical applications.

Abstract

A mathematical method for through-wall imaging via wave phenomena in the time domain is introduced. The method makes use of a single reflected wave over a finite time interval and gives us a criterion whether a penetrable obstacle exists or not in a general rough background medium. Moreover, if the obstacle exists, the lower and upper estimates of the distance between the obstacle and the center point of the support of the initial data are given. As an evidence of the potential of the method two applications are also given.