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In this communication, a semianalytical solution for the computation of the 2-D Green’s function for a cylindrical perfect electric conducting (PEC) enclosure containing an arbitrary number of confocal elliptic dielectric layers is provided. The approach relies on an expansion of the Green’s function into Mathieu functions, whose coefficients are found in an efficient way through a recursive procedure. The effectiveness of the technique is evaluated by comparisons with analytical formulas and against the results provided by independent numerical solvers. Moreover, the applicability of the solution to forward scattering problems using integral formulations is also assessed. In all the considered cases, the developed approach has been found to provide accurate results. [ABSTRACT FROM AUTHOR]

An iterative multiscaling approach for solving the electromagnetic inverse scattering problem related to the imaging of shallow subsurface targets with the ground-penetrating radar (GPR) is proposed. The approach combines the zooming properties of the multiscaling technique with the reconstruction capabilities of an Inexact-Newton (IN) method developed in $L^{p}$ spaces. It is based on multifrequency processing that allows one to face the ill-posedness of the inverse scattering problem by exploiting the regularization properties of a truncated Landweber (LW) method. Experimental data, extracted from radargrams obtained by the GPR in a real situation, are used for validation. The reconstruction results are also compared with those from competitive alternatives, such as a standard IN method or a state-of-the-art multifrequency Conjugate Gradient (CG)-based approach. [ABSTRACT FROM AUTHOR]

Stroke identification by means of microwave tomography requires a very accurate reconstruction of the dielectric properties inside patient’s head. This is possible when a precise measurement system is combined with a full nonlinear inversion method. In this article, the inversion of S-parameter data collected in a metallic chamber is performed with a nonlinear inversion strategy in Lebesgue spaces with nonconstant exponents. This is the first time that this kind of nonlinear S-parameter electromagnetic formulation has been applied to this problem. The inverse-scattering method incorporates a 2-D electromagnetic model of the imaging chamber based on a finite-element formulation, which has led to a complete redefinition of the solving procedure with respect to previous works. This allows a suitable description of the multistatic S-parameters due to the interactions between the incident radiation and the structure under test. The developed inversion procedure is first assessed by means of numerical simulations. The experimental results, obtained with a clinical microwave system prototype containing a liquid-filled 3-D SAM phantom with an inhomogeneity mimicking a hemorrhagic stroke, further prove the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

An increasing number of practical applications of three-dimensional microwave imaging require accurate and efficient inversion techniques. In this context, a full-wave 3D inverse-scattering method, aimed at characterizing dielectric targets, is described in this paper. In particular, the inversion approach has a Newton-based structure, in which the internal linear solver is a conjugate gradient-like algorithm in lp spaces. The presented results, which include the inversion of both numerical and experimental scattered-field data obtained in the presence of homogeneous and inhomogeneous targets, validate the reconstruction capabilities of the proposed technique. [ABSTRACT FROM AUTHOR]

An innovative nonlinear inverse scattering approach in variable exponent Lebesgue spaces is proposed for microwave imaging purposes. The main objective of the approach is to overcome one of the main problems associated with reconstruction procedures developed in Lebesgue spaces with constant exponent, i.e., the need for the selection of the optimum Lebesgue-space norm parameter, which is critical for obtaining accurate reconstructions, and no exact rules exist for this choice. The approach proposed in this paper is oriented to tomographic imaging applications at microwave frequencies, for which the adopted inversion procedure is based on a Gauss–Newton method, which has been reformulated in the unconventional variable exponent Lebesgue spaces. The capabilities of the approach are demonstrated by a set of numerical simulations, in which cylindrical dielectric targets are inspected. Moreover, an experimental result is reported. [ABSTRACT FROM AUTHOR]

A conjugate-gradient-based regularization technique in $L^{p}$ Banach spaces, in conjunction with an inexact-Newton solving scheme, is presented in this paper. The proposed method is applied to obtain the reconstruction of the dielectric properties of human tissues in hemorrhagic brain stroke microwave imaging. The dielectric reconstruction is obtained by solving a nonlinear inverse problem, starting from a set of scattered-field measurements. The presented numerical simulations with 2-D and 3-D anatomically realistic phantoms, as well as the preliminary experimental results, show that this method can be useful for retrieving the dielectric properties of the human head with a reduced over-smoothing effect in the final images. [ABSTRACT FROM AUTHOR]

A solution for the computation of the 2-D Green's function for a multilayer elliptic cylinder in the presence of a perfectly conducting core is reported. It extends a previous solution limited to dielectric layers only. The Green's function is computed by an efficient recursive procedure based on eigenfunction expansions in terms of Mathieu functions. Numerical results and comparisons are provided in order to validate the approach and to assess the effectiveness of the proposed solution. [ABSTRACT FROM PUBLISHER]

This letter deals with a recently proposed two-step algorithm for the reconstruction of dielectric and velocity profiles of axially moving cylinders. In particular, the aim of the present work is to investigate the limitations and capabilities in reconstructing the velocity profile. By considering a best-case scenario, it is shown that, although the algorithm should be able to work even in the presence of flows with very small axial velocity values, reliable results can only be obtained when the axial speed is larger than a lower bound. This bound is shown to be an intrinsic limitation of the algorithm which is only related to the cross-polarization isolation of the measurement system. Other simulations, based on worst-case scenarios, confirm that such a bound is independent of the type of flow considered, of the configuration of the measurement system, and of the errors coming from the step devoted to the reconstruction of the dielectric profile. Finally, the same simulations show that the algorithm is reliable in a wide range of speed values, provided sensors with large cross-polarization isolations are exploited. [ABSTRACT FROM PUBLISHER]

An electromagnetic inverse scattering approach for imaging of shallow subsurface objects is reported. It extends to multifrequency processing, an efficient method previously developed for single frequency imaging. The considered approach is an iterative procedure based on an inexact-Newton method developed in L^p Banach spaces, which exhibits effective regularization capabilities and reduced over-smoothing effects. The approach is validated using numerical simulations in which cylindrical scatterers are reconstructed in a homogeneous lossy medium. Results are compared with those obtained using standard single frequency operating conditions. [ABSTRACT FROM PUBLISHER]

Electromagnetic inverse scattering techniques are considered to reconstruct the permittivity and the velocity profiles of axially moving cylindrical targets. Two approaches are proposed. One of these is based on a two-step procedure. It is shown that it provides good approximations of the profiles to be reconstructed in a very efficient way, when the peak velocity is small with respect to the speed of light in vacuum. These features are obtained by neglecting the movement in the first step, which is devoted to the reconstruction of the geometric and dielectric properties of the cylindrical targets. The second approach is more classical and is defined as a global optimization problem. It is shown that the two procedures are in some way complementary in the sense that, when the two-step procedure can be applied, it is by far the best, with the general procedure giving large errors; vice versa, the two-step procedure is in trouble when the other one gives good results. In carrying out this analysis, some estimates on the effects of the movement on the scattered field components are deduced in the limit as the peak velocity goes to zero. [ABSTRACT FROM PUBLISHER]

A recursive solution for the computation of the two-dimensional Green's function for the multilayer elliptic cylinder is reported. It is based on the scattering solution by this canonical scatterer through eigenfunction expansions in terms of Mathieu functions. The paper reports the mathematical details of the approach as well as several validation tests and comparisons. [ABSTRACT FROM PUBLISHER]

A microwave imaging method previously developed for tomographic inspection of dielectric targets is extended to three dimensional objects. The approach is based on the full vector equations of the electromagnetic inverse scattering problem. The ill-posedness of the problem is faced by the application of an inexact-Newton method. Preliminary reconstruction results are reported. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of noise on a microwave axial tomograph developed by some of the authors for the inspection of dielectric objects. In particular, the impact of the measurement environment is considered and the images obtained from data measured in a controlled and an uncontrolled environment are presented and compared. Moreover, the effects of interference signals are considered. Accordingly, several experimental results are reported and discussed in terms of proper error parameters. [ABSTRACT FROM PUBLISHER]

In this paper, the development of a microwave axial tomograph for the inspection of dielectric materials is discussed. In particular, hardware and software solutions are pointed out. An experimental bistatic imaging setup is described. Moreover, the results of several forward-scattering simulations, which are aimed at defining suitable working conditions, are reported. Finally, to invert the collected field-scattered data, a deterministic inexact Newton method is applied. The approach is evaluated by using synthetic data, and the results of a preliminary experimental reconstruction are reported. [ABSTRACT FROM AUTHOR]

A new approach for the inversion of synthetic and measured scattered data is proposed in this paper. The approach is based on an iterative technique in which the nonlinear equations of the inverse-scattering problem are solved within the pth-order Born approximation. A regularization scheme based on an inexact-Newton method is applied. Several numerical simulations and experimental results are reported. Multiple separated dielectric cylinders are localized and reconstructed in a noisy environment. [ABSTRACT FROM AUTHOR]

A new approach to noninvasive inspection of dielectric targets at microwave frequencies is proposed. Cylindrical dielectric objects are reconstructed under the second-order Born approximation. A multi-illumination configuration is considered. The continuous model is discretized by the moment method and an efficient inexact-Newton method is applied. The dielectric profile is iteratively reconstructed starting from the measured scattered data, which are related to the unknown target through the inverse scattering equations written in a variational setting. Several numerical results are reported, which are aimed at assessing the capabilities of the approach in dealing with the nonlinear illeposed inverse problem associated to the short-range microwave imaging. Single, multilayer, and separate cylinders are reconstructed in noiseless and noisy environments. [ABSTRACT FROM AUTHOR]