Multi-frequency topological derivative for approximate shape acquisition of curve-like thin electromagnetic inhomogeneities

TL;DR

This paper presents a non-iterative, multi-frequency topological derivative imaging algorithm for accurately reconstructing the shape of thin electromagnetic inhomogeneities, especially cracks, in a homogeneous medium, validated through numerical simulations.

Contribution

The paper introduces a novel multi-frequency topological derivative method for imaging thin electromagnetic inclusions, extending its applicability to arbitrarily shaped cracks with improved accuracy.

Findings

Effective imaging of crack-like inclusions demonstrated in simulations.

Algorithm performs well with noisy data.

Multi-frequency approach enhances shape reconstruction accuracy.

Abstract

In this paper, we investigate a non-iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and/or magnetic permeability differ from those in the embedding (homogeneous) space. The main objective is the imaging of crack-like thin inclusions, but the algorithm can be applied to arbitrarily shaped inclusions. For this purpose, we apply multiple time-harmonic frequencies and normalize the topological derivative imaging function by its maximum value. In order to verify its validity, we apply it for the imaging of two-dimensional crack-like thin electromagnetic inhomogeneities completely hidden in a homogeneous material. Corresponding numerical simulations with noisy data are performed for showing the efficacy of the proposed algorithm.