Adriana Brancaccio

Information content of Born scattered fields: results in the circular cylindrical case

In this analysis some limitations of the linear Born approximation in the diffraction tomography problem from far-zone data are pointed out. The analysis is performed by means of singular-value decomposition of the scattering operator in the scalar two-dimensional case of a circular dielectric cylinder illuminated by a TM-polarized plane wave. It is shown that the validity of the Born approximation entails the important condition that the scattering object not present too-fast spatial variations of the permittivity profile. For the rotationally symmetric cylinder, evidence is presented that the imaginary part of the normalized scattered far field has no information content for real permittivity objects. Moreover, for angularly varying cylinders the information content of the scattered far field for a single view is approximately the same as in the multiview case. Examples of singular-value and singular-function behavior and of profile reconstruction are depicted for the considered geometries.

A Kirchhoff-Based Shape Reconstruction Algorithm for the Multimonostatic Configuration: The Realistic Case of Buried Pipes

A shape reconstruction algorithm is formulated for the multimonostatic configuration and the 2-D geometry. The imaging algorithm is based on the Kirchhoff approximation, works in the frequency domain, and exploits the singular value decomposition tool to achieve a stable solution. The effectiveness of the reconstruction algorithm is shown by processing synthetic data in the time domain generated via a finite-difference time-domain code. A performance analysis of the solution algorithm is addressed with varying host medium and measurement configurations, also by processing synthetic data for a 3-D geometry. Finally, an experimental validation of the technique is performed due to data collected by a time-domain ground-penetrating radar for buried pipe detection and localization.

Localization of the Interfaces of a Slab Hidden Behind a Wall

In this paper, a 1-D inverse-scattering problem laying within the framework of through-wall imaging is addressed. In particular, the problem of localizing the interfaces of a slab hidden behind an obstacle, another slab whose electromagnetic features and thickness are known, is considered. To this end, an approximate linear mathematical relationship between the scattered field and the unknown slab-interface positions is stated. Such an approximate relationship arises from neglecting the multiple-reflections between the two unknown slabs interfaces and between the slab and the obstacle. The unknown locations of the slabs interfaces are represented as the support of Dirac-delta functions, and the problem is cast as the inversion of a linear integral operator whose inversion is achieved by means of the Truncated-Singular-Value-Decomposition (TSVD) inversion scheme. The effect of the parameters of the obstacle on the inversion algorithm and the performances achievable by the solution approach are assessed by exploiting synthetic data. Furthermore, a comparison with the reconstructions obtained under the Born approximation and with the time-backscattered field is achieved. Finally, results obtained by employing experimental data collected owing to a stepped-frequency ground-penetrating radar system are also presented.

Shape reconstruction of perfectly conducting objects by multiview experimental data

This paper deals with the experimental validation of an algorithm, based on the Kirchhoff approximation, for the shape reconstruction of conducting objects from scattered field data. Measured data are collected in a controlled environment under a reflection mode with a finite observation domain and multiview/multistatic/multifrequency configuration. The results show the effectiveness of the approach which takes into account the view diversity by a simple strategy and a threshold procedure.

3D sliced tomographic inverse scattering experimental results

The problem of imaging three-dimensional strong scatter- ers by means of a two-dimensional sliced tomographic reconstruction algorithm is dealt with. In particular, the focus of the paper is on the experimental validation of the involved inversion algorithm thanks to measurements collected in a controlled environment. A simple strategy exploiting reconstructions obtained at difierent time instants in order to detect slowly moving scatterers is also experimentally validated.

ULTRA: Wideband Ground Penetrating Radar

The frequency range employed in ground penetrating radar (GPR) systems is generally limited to 2 GHz because media loss increases dramatically at higher frequencies. Nevertheless, a series of applications exists in the Cultural Heritage field where the development of high frequency systems would significantly benefit, in terms of resolution, from an increased operating band. This article presents ULTRA, a wideband GPR (800 MHz-4000 MHz) system, using a CW-SF technique developed for this type of surveying

TWI EXPERIMENTAL RESULTS BY A LINEAR INVERSE SCATTERING APPROACH

A through-wall imaging problem is tackled by means a linear inverse scattering approach described and numerically analyzed in previous works by the same authors. Here, such an approach is checked for against experimental data. To this end, a CW-SF ultrawideband radar system is used to take measurements in a controlled environment as well as for in situ experiments. Different types of scatterers and of obscuring walls are considered.

Multimonostatic Shape Reconstruction of Two-Dimensional Dielectric Cylinders by a Kirchhoff-Based Approach

The inverse problem of reconstructing the shape of dielectric cylinders by aspect-limited multimonostatic multifrequency electromagnetic scattering data is dealt with. The problem is formulated as a linear one by means of the physical-optics approximation distributional approach. The difference with respect to the case of perfectly electrical conducting scatterers is pointed out, since the penetrability of the scatterers is taken into account by considering the contribution of the “shadowed” side to the local reflection coefficient. The adopted model allows one to predict that both the “illuminated” and “shadowed” sides of the scatterer provide contribution to the reconstructed image but with a delocalization depending on the relative dielectric permittivity. The numerical results confirm this expectation and show the effectiveness of the approach.

Quadratic distorted approximation for the inverse scattering of dielectric cylinders

The nonlinear (quadratic) distorted approximation of the inverse scattering of dielectric cylinders is investigated, with the aim of pointing out the influence of the background medium. We refer to a canonical geometry consisting of a radially symmetric dielectric cylinder illuminated at a single frequency. We discuss how the spatial variations of those unknown dielectric profile functions that can be reconstructed by a stable inversion procedure are related to the permittivity of the background cylinder. First, results for the linear distorted approximation, obtained by means of the singular-value decomposition, are recalled and compared with the Born approximation. It turns out that the distorted model provides a smoother behavior of the singular values, and thus the inversion is more sensitive to the presence of uncertainties in the data. Furthermore, a stable inversion procedure can reconstruct only a very limited class of unknowns in correspondence with fast spatial variations related to the background permittivity and the excitation frequency. On the other hand, the quadratic model improves the approximation in the distorted case. This can be traced not only to the higher allowable level of permittivity but mainly to the fact that the model makes it possible to reconstruct different spatial features as the solution space changes. Numerical results show that the quadratic inversion performs better than the linear one for the same amount of uncertainty in the data.

Experimental validation of a PO-based shape reconstruction algorithm

The effectiveness of a linear inverse scattering algorithm for the shape reconstruction of perfectly conducting objects is experimentally validated by processing measured data. The data are collected via an automatic system for free-space measurements under reflection mode geometry. The amplitude and phase of the scattered field is measured in a multistatic and multifrequency configuration for different locations (views) of the transmitting antenna. The reliability of the measurement setup is shown by a comparison with simulated data. No a priori knowledge of the shape of the scatterers is assumed. The results of inversions of experimental data collected under single-view illumination agree well with those of inversions of synthetic data, so showing the robustness of the algorithm.