Processing the 2D and 3D Fresnel experimental databases via topological derivative methods

TL;DR

This paper introduces a one-step imaging method using topological derivatives and energies to reconstruct homogeneous targets from 2D and 3D Fresnel data, offering a faster alternative to existing techniques.

Contribution

The paper develops a novel topological derivative-based approach for electromagnetic inverse scattering, providing efficient closed-form expressions for 2D and 3D data reconstruction.

Findings

Approximations are comparable to existing methods.

Topological fields are easy to evaluate.

Method speeds up the reconstruction process.

Abstract

This paper presents reconstructions of homogeneous targets from the 2D and 3D Fresnel databases by one-step imaging methods based on the computation of topological derivative and topological energy fields. The electromagnetic inverse scattering problem is recast as a constrained optimization problem, in which we seek to minimize the error when comparing experimental microwave measurements with computer-generated synthetic data for arbitrary targets by approximating a Maxwell forward model. The true targets are then characterized by combining the topological derivatives or energies of such shape functionals for all available receivers and emitters at different frequencies. Our approximations are comparable to the best approximations already obtained by other methods. However, these topological fields admit easy to evaluate closed-form expressions, which speeds up the process.