Analysis of a multi-frequency electromagnetic imaging functional for thin, crack-like electromagnetic inclusions

TL;DR

This paper improves a multi-frequency electromagnetic imaging algorithm for detecting thin, crack-like inclusions by analyzing its structure and introducing a frequency-weighted functional, leading to enhanced imaging performance.

Contribution

It provides a detailed analysis of the imaging functional structure and proposes a frequency-weighted version that improves detection accuracy for thin electromagnetic inclusions.

Findings

The frequency-weighted imaging functional relates to Bessel functions of the first kind.

Numerical examples demonstrate improved imaging performance.

The method retains advantages of traditional algorithms while enhancing results.

Abstract

Recently, a non-iterative multi-frequency subspace migration imaging algorithm was developed based on an asymptotic expansion formula for thin, curve-like electromagnetic inclusions and the structure of singular vectors in the Multi-Static Response (MSR) matrix. The present study examines the structure of subspace migration imaging functional and proposes an improved imaging functional weighted by the frequency. We identify the relationship between the imaging functional and Bessel functions of integer order of the first kind. Numerical examples for single and multiple inclusions show that the presented algorithm not only retains the advantages of the traditional imaging functional but also improves the imaging performance.