Subspace migration for imaging of thin, curve-like electromagnetic inhomogeneities without shape information

TL;DR

This paper analyzes the mathematical structure of subspace migration techniques for imaging thin, curve-like electromagnetic inhomogeneities without prior shape information, and proposes improvements based on this understanding.

Contribution

It identifies the underlying mathematical structure of subspace migration without geometric assumptions and enhances the method using multi-frequency data.

Findings

Mathematical structure of subspace migration is characterized.

Multi-frequency approach improves imaging results.

Numerical simulations validate the proposed improvements.

Abstract

It is well-known that subspace migration is stable and effective non-iterative imaging technique in inverse scattering problem. But, for a proper application, geometric features of unknown targets must be considered beforehand. Without this consideration, one cannot retrieve good results via subspace migration. In this paper, we identify the mathematical structure of single- and multi-frequency subspace migration without any geometric consideration of unknown targets and explore its certain properties. This is based on the fact that elements of so-called Multi-Static Response (MSR) matrix can be represented as an asymptotic expansion formula. Furthermore, based on the examined structure, we improve subspace migration and consider the multi-frequency subspace migration. Various results of numerical simulation with noisy data support our investigation.