Recovery of small electromagnetic inhomogeneities from boundary measurements in time-dependent Maxwell's equations

TL;DR

This paper addresses the inverse problem of locating and characterizing small electromagnetic inhomogeneities within a domain using boundary measurements of the magnetic field over time, based on Maxwell's equations.

Contribution

It introduces a method to recover small electromagnetic inhomogeneities from boundary measurements in a time-dependent setting, advancing inverse problem techniques for Maxwell's equations.

Findings

Successful identification of inhomogeneities from boundary data

Development of a new reconstruction algorithm

Theoretical validation of the method's effectiveness

Abstract

We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the tangential component of the magnetic field on the boundary (or a part of the boundary) of a domain.