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

TL;DR

This work applies topological derivative and topological energy methods to the 2D and 3D Fresnel experimental databases to reconstruct homogeneous targets from microwave measurements. By formulating the inverse problem as a constrained optimization and exploiting closed-form topological fields derived from forward/adjoint Maxwell problems, the approach yields fast, one-step reconstructions that fuse multi-frequency data. The results show accuracy comparable to established methods in 2D, and demonstrate promising, though more challenging, performance in 3D, with clear guidance on when TD vs TE energies provide the strongest imaging cues. The methods require no a priori target information and leverage reciprocity and simple incident-wave modeling to achieve robust shape localization with low computational cost.

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.

Figures (27)

• Figure 1: Scaled representation of the location of the receiving and emitting antennas for a generic experiment, as well as the size of the inspection zone compared with the size of the objects' section.
• Figure 2: Horizontal sections of the five different targets compared with the inspection zone. The first two ones are made of dielectric material (indicated by a dotted pattern) whereas the last three ones are metallic targets (homogeneous pattern).
• Figure 3: Measured incident field (dots) for the experiments performed at a low frequency $2\,\mathrm{GHz}$ and fitted field (line). The amplitude is largest at the furthest receivers ($\theta^\mathrm{R}=\pi$) which suggests a highly directional antenna.
• Figure 4: (a) Incident field fitted by a series of Hankel functions for $2\,\mathrm{GHz}$. Notice the directionality of the antenna, as well as the resemblance of the incident wave to a plane wave near the objects. (b) Incident field fitted for the frequency $16\,\mathrm{GHz}$. Now the field is far from isotropic.
• Figure 5: (a)-(c) Incident electric field for the three wave models at $2\,\mathrm{GHz}$. (d)-(f) Incident electric field for the three wave models at $16\,\mathrm{GHz}$.