A direct sampling method for inverse time-dependent electromagnetic source problems: reconstruction of the radiating time and spatial support

TL;DR

This paper introduces a direct sampling method to reconstruct both the temporal and spatial support of electromagnetic sources from multi-frequency measurements, improving source localization accuracy.

Contribution

The paper presents a novel approach that simultaneously reconstructs the source's radiating time and spatial support using multi-frequency data, advancing beyond existing methods.

Findings

Successfully reconstructs the radiating time of sources.

Accurately determines the spatial support region.

Validates the method with 3D numerical examples.

Abstract

This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic system with a frequency-dependent source term. We propose a novel direct sampling method for reconstructing such radiating time and spatial space of sources from multi-frequency far-field measurements. By using a pair of multi-frequency data from opposite observation directions, we can obtain the radiating time of the signal. Based on this, the smallest region between two hyperplanes containing the support of source can be reconstructed using multi frequency data from one observation direction. The Theta convex hull of the source support can be reconstructed from multi-frequency data from sparse observation directions. Compared with existing sampling methods that mainly focus on reconstructing the spatial support, the proposed approach allows for the simultaneous reconstruction of both spatial and temporal features of the source.Three-dimensional numerical examples are conducted to validate the effectiveness of the algorithm.