Reconstruction of thin electromagnetic inhomogeneity without diagonal elements of a multi-static response matrix

Abstract

This paper aims to shape the identification of thin inhomogeneities with different dielectric/magnetic properties from a two-dimensional homogeneous background. The shapes are identified through subspace migration without requiring the diagonal elements of the collected multi-static response matrix. To understand why subspace migration without diagonal elements can retrieve the shape of a thin inhomogeneity, we carefully investigate the relations between the imaging function and Bessel functions of orders 0 and 1. This analysis exploits the fact that when a thin homogeneity exists, the measured far-field pattern can be represented as an asymptotic expansion formula. The investigated relation is supported in numerical experiments with noisy data.

Fast Localization of Small Inhomogeneities from Far-Field Pattern Data in the Limited-Aperture Inverse Scattering Problem

“…As such, based on the singular-value decomposition of the MSR matrix, we generated an appropriate test vector consisting of the incident field at each search point before we used the orthonormal property of the left-and right-singular vectors of the MSR matrix and present a method for designing the indicator functions for localizing the inhomogeneities. In terms of the related works on sampling-type imaging techniques, we refer to [13][14][15][16] for subspace migration, refs. [17][18][19][20] for the linear sampling method, refs.…”

Real-time microwave imaging of unknown anomalies via scattering matrix

“…Recently, the MUSIC algorithm and direct sampling method for identifying the location of the dielectric anomaly from scattering parameters collected by a small number of dipole antennas has been developed when the diagonal elements of the scattering matrix or scattering parameter with the same transducer and receiver location are measurable [44,45]. In [46], subspace migration for imaging of thin inhomogeneity without diagonal elements of so-called multi-static response (MSR) matrix whose elements are far-field pattern has been concerned. However, to the best of our knowledge, there are no theoretical results of subspace migration for real-world imaging an unknown anomaly when scattering parameter data is collected and affected by a small number of dipole antennas.…”