Two Single-shot Methods for Locating Multiple Electromagnetic Scatterers

TL;DR

This paper introduces two efficient, noise-robust inverse scattering methods for locating multiple electromagnetic scatterers using a single far-field measurement, applicable to various obstacle sizes and types.

Contribution

The paper presents two novel single-shot schemes for electromagnetic scatterer localization, accommodating unknown numbers and types of obstacles with rigorous mathematical validation.

Findings

Effective localization of small and regular-sized scatterers

Methods are robust to noise and do not require inversion

Numerical experiments confirm accuracy and efficiency

Abstract

We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting plane wave. The first scheme is for locating scatterers of small size compared to the wavelength of the detecting plane wave. The multiple scatterers could be extremely general with an unknown number of components, and each scatterer component could be either an impenetrable perfectly conducting obstacle or a penetrable inhomogeneous medium with an unknown content. The second scheme is for locating multiple perfectly conducting obstacles of regular size compared to the detecting EM wavelength. The number of the obstacle components is not required to be known in advance, but the shape of each component must be from a certain known admissible class. The admissible class may consist of multiple different reference obstacles. The second scheme could also be extended to include the medium components if a certain generic condition is satisfied. Both schemes are based on some novel indicator functions whose indicating behaviors could be used to locate the scatterers. No inversion will be involved in calculating the indicator functions, and the proposed methods are every efficient and robust to noise. Rigorous mathematical justifications are provided and extensive numerical experiments are conducted to illustrate the effectiveness of the imaging schemes.