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

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.

Multifrequency Linear Sampling Method on Experimental Datasets

“…11. It is interesting to note that the reconstructed scatterers are slightly rotated from the published exact case, and this has been noticed too in [16] and [23]. It is also interesting to emphasize that the product indicator again sharpens the reconstruction.…”

Multifrequency Topological Derivative Approach to Inverse Scattering Problems in Attenuating Media

“…When real experimental data are processed, noise is inevitably present. The reconstructions obtained in [23,45] evidence the robustness of the method when dealing with experimental data. For our inverse scattering problem in an attenuating half space, we have checked that increasing the level of noise δ defined in (8) from δ = 0.01 to δ = 0.1 results are almost identical.…”

“…When the material properties of the objects are unknown, we could generate initial approximations to their geometry by related topological energy techniques [45,[50][51][52] and to their material parameters by hybrid gradient methods [38]. Uncertainty due to noise can be addressed by combining topological priors with Bayesian techniques [46].…”

Exploring the performance of the topological energy method for object and damage detection from noisy and poor databases

“…This choice guarantees that the maximum of each term in equation (3.7) is equal to 1 and has been previously successfully used in other papers (see, for instance, [15,18,21]). However, there are other alternatives for weighting contributions that could be explored.…”