Fourier method for identifying electromagnetic sources with multi-frequency far-field data

TL;DR

This paper introduces a non-iterative Fourier-based method for reconstructing unknown electromagnetic sources from multi-frequency far-field data, providing theoretical guarantees and demonstrating effectiveness through numerical experiments.

Contribution

A novel Fourier coefficient recovery approach for electromagnetic source identification with proven uniqueness and stability.

Findings

The method accurately reconstructs sources from simulated data.

The approach is computationally efficient and stable.

Numerical experiments validate the effectiveness of the method.

Abstract

We consider the inverse problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse problem from far-field measurements. The method is based on recovering the Fourier coefficients of the unknown source. A key ingredient of the method is to establish the relationship between the Fourier coefficients and the multi-frequency far-field data. Uniqueness and stability results are established for the proposed reconstruction method. Numerical experiments are presented to illustrate the effectiveness and efficiency of the method.