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This paper addresses the problem of reconstructing geometrical features of 3-D targets embedded into a nonaccessible region from multiview multistatic scattered field data. Sampling methods (SM) are simple and computationally effective approaches to pursue this task. However, their implementation requires a large number of multipolarization sources and probes. Moreover, their performances are often unsatisfactory for aspect-limited measurement configurations and lossy media. In order to tackle these drawbacks, usually faced in subsurface imaging, we propose a simplified and improved formulation based on the physical interpretation of SM. In particular, such a formulation relies on a small number of single polarization probes and exploits multifrequency data, for the first time in the framework of SM. The performances of the resulting approach are verified by monitoring 3-D regions of large extent. Index Terms--Electromagnetic scattering inverse problems, factorization method (FM), linear sampling method (LSM), microwave imaging, subsurface imaging.

Starting from the concept of 'degree of non-linearity' of the relationship amongst unknown parameters and scattered fields, we discuss how knowledge of the geometrical features of the targets favorably affects the solution of inverse scattering problems. The same concept is also exploited to optimize the contrast source-extended Born (CS-EB) model, resulting in the optimized CS-EB (O-CS-EB) inversion approach, which remarkably reduces false solutions occurrence. Then, a two-steps approach is proposed as a reliable and effective inversion strategy. The first step consists in retrieving the shape of the targets using the linear sampling method, while in the second step, the estimated shapes and the O-CS-EB are exploited to reconstruct the permittivity profile. The approach has been tested against experimental data, showing that very accurate reconstructions are achieved from monochromatic data. Index Terms--Contrast source-extended Born (CS-EB), electromagnetic inverse scattering problems, shape reconstruction.

Efficient and reliable reconstruction of location and shape of dielectric targets via microwave imaging is relevant in many applications. In this respect, the linear sampling method is an effective candidate to pursue this task. However, despite its simplicity and computational effectiveness, still its use is restricted to the mathematical community wherein it has been originally developed. Starting from this observation, in this paper we propose and test a simple and original 'physical' interpretation of the linear sampling methods, which shows its relationship with electromagnetic focusing problems. Taking advantage of this result we discuss merits and limitations of the method and suggest new guidelines for a successful application. The analysis is supported with results against experimental data. Index Terms--Electromagnetic scattering inverse problems, linear sampling method (LSM), shape reconstruction.

A new, simple, and fast method for the solution of electromagnetic scattering problems for perfectly conducting objects of arbitrary shape is presented. The method is based on an equivalent representation of the conducting object in terms of a circular one having a higher order impedance boundary condition on its surface. As a first result, a new universal relation between the higher order surface impedances and the shape of the object is obtained. Then, by taking advantage of this relationship, the scattering problem related to a conducting object is recast as the solution of a matrix equation whose coefficients are determined from the higher order impedances. Numerical simulations show that the method yields to accurate results, and that, it is computationally effective. Index Terms--Electromagnetic scattering, impedance boundary condition (IBC), numerical methods.

Accurate and reliable evaluation of the electromagnetic field scattered by dielectric objects is a canonical problem in the electromagnetic community. In the framework of integral equation formulations, iterative techniques, and in particular conjugate gradient (CG) schemes, are widely used. However, when the number of parameters grows, CG techniques may become too demanding from a computational point of view. In this paper, we show that many forward scattering problems can be conveniently solved by means of very simple series expansions, which allow a lower computational complexity and memory storage with respect to other iterative schemes. In particular, we consider three different series expansions, namely: 1) the traditional Born series; 2) the contrast source-extended Born series, which is recently introduced by rewriting the traditional source-type integral equations; and 3) a new series, which is a hybridization of the previous ones. Theoretical conditions for the applicability of the series expansions are discussed, and practical tools to foresee that a problem can be solved by means of these simple iterative schemes are provided. Numerical examples are reported for the sake of comparison and to assess performance. Index Terms--Contrast source extend Born model, electric field integral equation, electromagnetic scattering, integral equations.

In this paper, we investigate whether and how one can synthesize given far field patterns by acting on the dielectric profile of a lens antenna. In particular, an approach to design a radiating system consisting of a variable dielectric profile and a single or a low number of feeds is proposed and discussed. To properly take into account physical and practical feasibility issues, the proposed method splits the problem into two steps. The first one is aimed to fix design goals (i.e., the nominal field), in such a way to avoid super-directive or physically unfeasible antennas and properly exploits known properties of electromagnetic fields radiated by finite extent sources. The second step, dealing with the dielectric profile synthesis, is based on suitable modifications of inverse scattering techniques and can take into account constraints on the spatial behavior as well as of dielectric characteristics of the profile to be synthesized. To show the interest of the subject, as well as effectiveness of the proposed approach, the synthesis of new dielectric antennas, such as a high directivity source and a lens radiating a steerable degradation-free Chebyshev pattern, is considered in the two dimensional scalar case. Index Terms--Antenna theory, antennas synthesis, inverse scattering, lens antennas, shaped beam antennas.

This work presents the design and numerical assessment of a novel microwave imaging (MWI) system, capable of providing a full 3-D image of food/beverage products content in order to disclose the possible presence of physical contaminants, such as plastic fragments. The system here presented exploits the dielectric contrast between the food content and possible intrusions at microwave frequencies; it is based on an antenna array architecture inspecting the items in motion along a conveyor belt without interrupting the production process. The inversion problem is solved by means of linearization, assuming the viability of the Born approximation thanks to the localized intrusions, and regularization, based on the singular value decomposition of the discretized scattering operator. Furthermore, an algorithm, to balance the illumination of the considered scenario due to the nonuniform radiation of the employed antennas, is presented to enhance imaging. The system is first assessed considering an ideal case and then extended to a more realistic approach, for two different kinds of food products, with completely different dielectric properties and considering the performance of existing instrumentation for the purpose. The obtained results lay the foundations for the realization of an actual prototype. [ABSTRACT FROM AUTHOR]

In inverse scattering problems, only a limited amount of independent data is actually available whenever the finite accuracy of the measurement set up is taken into account. In this paper, we deal with the problem of quantifying such an amount in the subsurface sensing case. In particular, an alternative formulation of the problem is given which also allows to understand how to dimensionate the measurement setup in an optimal fashion. Analytical results are reported for the case of a lossless soil, while a numerical study is carried out in the general case. By relying on the same formulation and tools, we also discuss the kind of unknown profiles that can actually be retrieved. In particular, it is shown that the class of retrievable functions exhibits intrinsic multiresolution features. This suggests that adoption of wavelet expansions to represent the unknown function may enhance the reconstruction capabilities. Numerical examples support this conclusion. Index Terms--Electromagnetic scattering, ground penetrating radar, inverse scattering, microwave tomography, nonlinear inverse problems.