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Field sampling should be devised to preserve the information required for the knowledge of the radiation of an antenna. In this paper, we introduce a sampling scheme based on an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

Proper field sampling strategies are important in antenna measurements and diagnostics applications to reduce the overall testing time. We investigate the role of source dimension in determining sampling points’ locations by referring to circumference geometries. An inverse problem approach is adopted, and spectral decomposition of the relevant operator is considered for a 2-D geometry. First, we introduce and discuss an approximation of the resulting point spread functions (PSFs), on which we found our approach. Next, a numerical strategy to discretize the field observation domain is presented, which results in a nonuniform angular step depending, in turn, on source extension. Some numerical examples of source characterization show the effectiveness of the approach in comparison to uniform angular sampling. [ABSTRACT FROM AUTHOR]

The role of the source geometry in the radiation of focusing beams by conformal antennas is examined by the comparison of their directivity functions at different maximum directions. An inverse source problem approach is adopted, where solutions stable with respect to data uncertainties are to be found by relying on the analysis of the pertinent operator by the Singular Values Decomposition. This general framework allows to connect the mean value of the maximum directivity function to the Number of Degrees of Freedom of the conformal source, which depends only on its electrical length. For each source geometry the focusing far field ensuring the maximum directivity for every pointing direction and the corresponding source current are obtained. The comparison with the ones achieved by the usual phase compensation technique of the source current reveals their optimal behavior. The usefulness of the approach as a tool in antenna synthesis is shown by comparing different geometries for those applications where identical beams are required to be radiated for the coverage of a large angular domain.

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]

An efficient multiresolution inverse scattering approach is presented for profiling high-contrast buried targets in large investigation domains (IDs). The proposed technique is based on an iterative multiscale approach (IMSA) that starts with coarse meshes and successively zooms in and marches toward the detected target location. Hence, by tightening the ID, the resolution could be enhanced without any increase in the number of meshes of the search domain. Here, the global evolutionary programming (EP) optimization algorithm is used in each step of IMSA, to guarantee the success of inversion process. In particular, an efficient variation in EP with Cauchy mutation is implemented for enhanced convergence. Moreover, a hybrid combination of multifrequencies (MFs) and frequency hopping (FH) schemes is combined with the proposed technique to better deal with the problem’s nonlinearity and also simultaneously make a consistent trade-off between mesh length and frequencies. The proposed FH-MF-IMSA is evaluated by implementing it to various large-scale subsurface problems. Furthermore, the superior performance of this technique is shown by comparing its results with the standard IMSA, as well as with other well-known global optimization techniques. [ABSTRACT FROM AUTHOR]

An inverse problem approach is adopted to investigate the role of a limited observation domain in conformal source radiation both in the far and near zones. The spectral decomposition of the relevant operator drives the investigation, especially by the discussion of the singular values’ behavior and the point spread function (PSF). For a circular source geometry, accurate closed-form evaluations of the PSF allow to establish its angular variant behavior for limited observation angular domains. This leads to introducing a numerical procedure, based on the widths of the PSF main lobes, able to define an optimal source discretization, that is, the spacing of the array elements whose radiated field has the same number of degrees of freedom of the continuous conformal source. A nonuniform spacing is derived and the performances of the corresponding conformal arrays are compared with the uniform case, the number of elements being equal. Numerical results of pattern synthesis and array diagnostics of faulty elements support the improvement achieved by the approach when the same number of array elements are located in a nonuniform pattern. [ABSTRACT FROM AUTHOR]

Linear arrays have been well studied for their widespread applications, but they suffer from severe limitations in the scanning capabilities due to the inherent main beam spreading. The combination of two linear arrays, radiating simultaneously, may provide the coverage of a wide angular domain by identical beams. More in general, first, we consider the radiation properties of a collection of continuous linear sources by following an inverse source approach which aims at investigating the spectral decomposition of the relevant radiation operator by discussing its singular value decomposition and the number of degrees of freedom of the source according to its geometry. Then, a connection with the known closed-form results of the single line case is established. Next, for an angle geometry, the discussion of the point spread function reveals the condition to be achieved for an angle source to radiate identical beams with a coverage larger than the one of a single linear source with the same total length. Finally, we consider the power synthesis of identical focusing beams by linear arrays, arranged in an angle geometry, also including the effect of the element factor, without excitation constraints, so to show how possibly to drive the design of electrically large arrays by such an analytical approach. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm for retrieving all the second statistical moments of the sea surface that affect the scattering of waves at small angles of incidence. A feature of this algorithm is the analysis of the spectral characteristics of the reflected waves only, without taking into account the backscattering cross section. The analysis of the width and the shift of the Doppler spectrum (DS) allows us to use the obtained algorithm without the preliminary instrumental calibration, which is necessary for the backscattering cross section. We give final expressions for calculating the width and the shift of the DS in the monostatic problem statement for small angles of incidence. We obtain the expressions within the framework of the Kirchhoff approximation, which makes them reliable only in the quasi-specular reflection region. Features of these formulas are the description of the surface by five statistical moments of the second order and taking into account the anisotropic antenna pattern (AP). To solve the inverse problem of retrieving sea surface parameters, we propose a measurement scheme including three motionless transceiver antennas with different APs. For this measurement scheme, we give analytical expressions for all five unknown parameters of surface waves. Also, we give a theoretical analysis of the accuracy of the algorithm obtained for different wind speeds and wind directions. All the results are valid for the scattering of both acoustic and electromagnetic waves. [ABSTRACT FROM AUTHOR]

A broadband soil dielectric spectra retrieval approach (1MHz--2GHz) has been implemented for a layered half space. The inversion kernel consists of a two-port transmission line forward model in the frequency domain and a constitutive material equation based on a power law soil mixture rule (Complex Refractive Index Model--CRIM). The spatially-distributed retrieval of broadband dielectric spectra was achieved with a global optimization approach based on a Shuffled Complex Evolution (SCE) algorithm using the full set of the scattering parameters. For each layer, the broadband dielectric spectra were retrieved with the corresponding parameters thickness, porosity, water saturation and electrical conductivity of the aqueous pore solution. For the validation of the approach, a coaxial transmission line cell measured with a network analyzer was used. The possibilities and limitations of the inverse parameter estimation were numerically analyzed in four scenarios. Expected and retrieved layer thicknesses, soil properties and broadband dielectric spectra in each scenario were in reasonable agreement. Hence, the model is suitable for an estimation of in-homogeneous material parameter distributions. Moreover, the proposed frequency domain approach allows an automatic adaptation of layer number and thickness or regular grids in time and/or space. [ABSTRACT FROM AUTHOR]

An iterative subsurface inverse scattering algorithm has been proposed to profile high-contrast 2-D dielectric objects buried under a lossy ground. The proposed iterative modified diffraction tomography (IMDT) method is based on the combination of the traditional iterative Born method and DT technique which is well known for its simplicity and robustness. In effect, IMDT is an iterative Born algorithm that utilizes the spectral domain concept of DT for solving the inversion problem. The proposed iterative approach results in removing the Born approximation’s limitation of DT technique in dealing with high-contrast scatterers. To this end, the total field inside the reconstruction domain is renewed and then expanded into upgoing and downgoing plane waves in each iteration. Consequently, by exponential expansion of the fields and deriving a modified DT formulation, high-contrast targets are also efficiently reconstructed. To assess the proposed IMDT method, various high-contrast objects and noise conditions are studied. It is shown that the IMDT algorithm significantly outperforms the DT technique and is capable of reconstructing high-contrast objects efficiently and accurately even in noisy environments. [ABSTRACT FROM AUTHOR]

An efficient method based on the evolutionary programming (EP) technique is proposed for inverse profiling of 2-D buried dielectric objects with elliptical cross sections. In particular, EP with Cauchy mutation operator (EP-CMO), as its first reported implementation to inverse problems, is utilized as a stochastic optimization tool for quantitatively reconstructing buried objects. Moreover, the method of moments technique in conjunction with conjugate gradient-fast Fourier transform method is used, as a fast and simple frequency domain forward solver, in each iteration of the proposed method. Numerical results for different case studies are presented and analyzed. To assess the proposed EP-CMO method, the results are also compared statistically with that of three other well-known optimization techniques, namely, EP with Gaussian mutation, particle swarm optimization, and genetic algorithms. The results reveal that EP-CMO is a significantly more robust and efficient optimization tool in reconstruction of this class of buried objects. [ABSTRACT FROM PUBLISHER]

A simple and effective two-step method to detect and localize scattering objects from the measurements of the total electric field, collected at a single frequency on a planar domain, is presented. The first step consists in solving a linear inverse source problem, looking for surface equivalent currents on a plane located between the measurement surface and the objects themselves. Thus, the equivalent currents associated with both the scatterer presence and the background contribution are obtained. In the second step, the support of the equivalent currents associated with the objects is separated from the background by exploiting the low-rank property of the background field. The proposed method does not require information on the source, except for its frequency, and it is easily implementable and entails a low computational burden. Experimental results validate the method. [ABSTRACT FROM PUBLISHER]

The Cole-Cole (C-C) models have been frequently used for a precise description of the dispersion characteristics of biological tissues. One of the main difficulties in the direct reconstruction of these dielectric properties from time-domain measurements is their frequency dependence. In order to overcome this difficulty, an electromagnetic (EM) inversion technique in the time domain is proposed, in which four kinds of frequency-independence model parameters, the optical relative permittivity, the static conductivity, the relative permittivity difference, and the relaxation time, can be determined simultaneously. It formulates the inversion problem as a regularized minimization problem, whose forward and backward subproblems could be solved iteratively by the finite-difference time-domain (FDTD) method and any conjugate gradient algorithm, respectively. Numerical results on two types of stratified C-C slabs, with smooth and discontinuous parameter profiles, respectively, confirm the performance of the inversion methodology. [ABSTRACT FROM AUTHOR]

A hybrid method is proposed to locate the boundaries and determine the dielectric constants of multiple homogeneous scatterers by postprocessing the results of the linear sampling method (LSM). The hybrid method is composed of three steps combining the capabilities of the LSM, the multiple signal classification (MUSIC) algorithm, and the generalized multipole technique (GMT). Initially, a new measure of the noise level of the multistatic response (MSR) matrix is proposed. Subsequently, the LSM is applied using the Tikhonov regularization. Then, the scattered field is back-propagated into the investigation domain using the GMT, where in order to ensure the stability, a MUSIC-based approach is exploited to determine the optimum reconstructing multipole sources. The case of limited scattered field data is also addressed by introducing a modification of the Papoulis–Gerchberg algorithm (PGA). Finally, the boundary and the dielectric constant of each scatterer are obtained simultaneously by solving an inverse boundary value problem through an optimization. The proposed hybrid approach is capable of efficiently approximating the dielectric constant of multiple homogeneous dielectric scatterers in a parallel manner. The effectiveness of the proposed method and the accuracy of the solutions are demonstrated by applying the method to both numerical and measured data. [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]

We exploit the sparseness of induced currents on the surfaces of obscured perfectly conducting (PEC) scatterers in developing a single-frequency imaging algorithm in 2-D space. We model the induced currents on the targets by a set of unknown filament currents to which we apply the surface-equivalence theorem. We use l1 regularization to promote the solutions with a small number of equivalent sources placed in the vicinity of scatterer surfaces. The restored equivalent sources accurately determine the illuminated portions of the scatterer contours. We compare the performance of the algorithm with that of linear sampling (LSM) and MUSIC. We verify the proposed algorithm on the equivalent 3-D experimental model. [ABSTRACT FROM PUBLISHER]

An iterative technique for the reconstruction of longitudinally inhomogeneous lossy dielectric material loaded in a uniform metallic waveguide is addressed in this paper. The problem is first formulated as an inverse scattering one based on an integral equation in terms of the unknown complex permittivity. By using knowledge of scattering parameters, the Gauss–Newton technique is employed to solve the inverse problem with both the Tikhonov regularization and multiplicative regularization. In order to show the effectiveness of the method, it is tested against numerical and experimental data at X- and K-bands and satisfactory reconstructions are obtained. Experimental results show that the inverse algorithm with multiplicative regularization can be used for the characterization of multilayered structures in a waveguide without needing a priori information. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

The problem of imaging 3-D perfect electric conducting objects from scattered field measurements is addressed. Plane waves at a fixed angle of incidence and varying frequency provide the illuminating radiation whereas the scattered field is collected in far-field zone. The physical optics approximation is adopted to simplify the scattering model and the scatterers' shapes (i.e., their contour surfaces) are described as the support of d distributions. This leads to a linear integral relationship between the scattered field and the unknown distributions, the linear distributional model, which is inverted by employing its singular value decomposition. Emphasis is placed on the study of the dyadic operator to be inverted which links the vector unknown to the scattered field vector and on the role of the polarization diversity. In particular, three different approaches are presented and compared from the computational as well as the resolution point of view. The analysis is performed numerically by means of synthetic data generated by a finite-element-method-based forward solver. [ABSTRACT FROM AUTHOR]

This paper presents recent advances in a 3-D inverse scattering technique, called forward-backward time-stepping (FBTS), applied to the reconstruction of the microwave properties of the breast. The FBTS algorithm is utilized for a numerical-based study of a 3-D breast model based on an Mill. Several illumination schemes, based on different microwave transmitter/receiver configurations, are compared based on the quality of the reconstructed images of the breast model. A combination of cylindrical and planar arrays is shown to provide accurate estimates of the model electrical parameters that delineate the various regions of the breast. Although further analysis with this combination array demonstrates that tumors of reduced size and reduced contrast with the surrounding fibroglandular region are much more difficult (and in some cases not possible) to reconstruct, the study presents some promising initial results of a reconstruction technique for breast imaging and cancer detection. [ABSTRACT FROM AUTHOR]

For 2D transverse magnetic (TM) microwave inversion, multiplicative-regularized contrast source inversion (MR-CSI), and the distorted Born iterative method (DBIM) are compared. The comparison is based on a computational resource analysis, inversion of synthetic data, and inversion of experimentally collected data from both the Fresnel and UPC Barcelona data sets. All inversion results are blind, but appropriate physical values for the reconstructed contrast are maintained. The data sets used to test the algorithms vary widely in terms of the background media, antennas, and far/near field considerations. To ensure that the comparison is replicable, an automatic regularization parameter selection method is used for the additive regularization within the DBIM, which utilizes a fast implementation of the L-curve method and the Laplacian regularizer. While not used in the classical DBIM, we introduce an MR term to the DBIM in order to provide comparable results to MR-CSI. The introduction of this MR term requires only slight modifications to the classical DBIM algorithm, and adds little computational complexity. The results show that with the addition of the MR term in the DBIM, the two algorithms provide very similar inversion results, but with the MR-CSI method providing advantages for both computational resources and ease of implementation. [ABSTRACT FROM AUTHOR]

The microwave imaging system currently being developed at the Technical University of Denmark is described and its performance tested on simulated data. The system uses an iterative Newton-based imaging algorithm for reconstructing the images in conjunction with an efficient method-of-moments solution of the associated forward scattering problem. A cylindrical multistatic antenna setup with 32 horizontally oriented antennas is used for collecting the data. It has been found that formulating the imaging algorithm in terms of the logarithm of the amplitude and the unwrapped phase of the measured signals improves its performance when compared to the more commonly used complex phasor formulation. This improvement is illustrated by imaging a simulated hemispherical breast model using both formulations. In addition to this, the importance of using the correct position and orientation of the antennas in the measurement system is shown by imaging the same breast model using a measurement setup in which the antennas are vertically oriented. [ABSTRACT FROM AUTHOR]

An enhanced multistep strategy based on a multiresolution particle swarm optimizer is proposed for 3-D microwave imaging. The aim of such an integration is to improve the convergence capabilities of the approach and to reduce the dimension of the search space and the computational burden of the optimization strategy, thanks to a constrained control of the particle velocities adaptively determined. This favors the exploitation of the global search capabilities of the particle swarms also in the framework of large-scale 3-D inverse scattering problems. The proposed technique is assessed by considering numerical tests concerned with single and multiple 3-D targets. The results of an experimental testing are also discussed. [ABSTRACT FROM AUTHOR]

One of the applications of microwave tomography, which recovers the dielectric profiles based on the scattered-field data, is the detection of breast cancers. Here, we propose a new method, which aims to collect thermoacoustic signals generated during the period of microwave illumination, and use them for construction of the finite-element mesh for microwave tomography. Our preliminary two-dimensional study carefully links the physical processes that underlies this hybrid detection approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Forward-backward time-stepping is a unique approach for solving electromagnetic inverse scattering problems in the time domain. In this paper, the technique is applied to a realistic, heterogeneous breast model. The ability to detect a 5-mm diameter malignancy and provide substantial quantitative information about the breast's composition is demonstrated. [ABSTRACT FROM PUBLISHER]

Breast-cancer screening using microwave imaging is emerging as a new promising technique as a supplement to X-ray mammography. To create tomographic images from microwave measurements, it is necessary to solve a nonlinear inversion problem, for which an algorithm based on the iterative Gauss-Newton method has been developed at Dartmouth College. This algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the Tikhonov algorithm. In this paper, a new algorithm for determining the iteration update values in the Gauss-Newton algorithm is presented which is based on the conjugate gradient least squares (CGLS) algorithm. The iterative CGLS algorithm is capable of solving the update problem by operating on just the Jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations. The new algorithm is compared to the Gauss-Newton algorithm with Tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A genetic programming-based method for the imaging of two-dimensional conductors is presented. Geometry is encoded in this scheme using a tree-shaped chromosome to represent the Boolean combination of convex polygons into an arbitrary two-dimensional geometry. The polygons themselves are encoded as the convex hull of variable-length lists of points that reside in the terminal nodes of the tree. A set of genetic operators is defined for efficiently solving the inverse scattering problem. Specifically, the encoding scheme allows for a standard genetic programming crossover operator, and several mutation operators are designed in consideration of the encoding scheme. Several results are presented that demonstrate the method on a number of different shapes [ABSTRACT FROM PUBLISHER]

We present an inverse scattering approach for the bulk electromagnetic characterization of composite materials, based on a prior proof that artificial metallo-dielectric photonic crystals can be described by effective highly resonant response functions in a wide frequency range, including several passbands/bandgaps. The method becomes complete and unambiguous at high frequencies by employing the analytic continuation of the optical path length and a consistency criterion to ascertain the physical meaning of the extracted effective parameters. It may also be used as a fast simulator or as a measurement-based predictor of the performance of multilayered structures using the scattering matrix (simulated or measured) of a single monolayer of that material. The approach is applied for the characterization of metamorphic materials, which are recently introduced artificial structures that exhibit distinct macroscopic states of behavior as far as the reflected electromagnetic field is concerned. According to interconnect topologies of their scatterers, they appear, at a single frequency, as electric conductors, absorbers, amplifiers, and passive or active magnetic conductors. Detailed evaluations are given of the complex dispersive wave impedance, refractive index, and permittivity and permeability functions for each metamorphic state of a specific three-state metamorphic material. It is found that, as a rule, the electric and magnetic wall states are related to resonant permittivity and permeability values, respectively. Furthermore, the analysis reveals broad regions with negative values of permittivity or permeability. Both resonant and negative values of εeff, μeff occur within bandgaps or at band-edges. Finally, the approach is applied to the negative refractive index metamaterial composed of a cylinder and two split-ring resonators, which reveals the existence of a high-frequency band with negative group velocity. [ABSTRACT FROM AUTHOR]

This paper deals with the application of a frequency-domain microwave-tomography-imaging algorithm to a multibistatic configuration in ground-penetrating-radar applications. First, the authors formulate the inverse problem as a linear one by exploiting the Born approximation. Then, the reconstruction capabilities of the solution algorithm are investigated, and an optimal frequency step to be adopted for the reconstruction is discussed and determined. Finally, inversion results are presented with synthetic data obtained from time-domain simulations and then Fourier transformed in frequency domain. [ABSTRACT FROM AUTHOR]

We consider the three-dimensional electromagnetic inverse scattering problem of determining information about a coated object from a knowledge of the electric far-field patterns corresponding to time harmonic incident plane waves at fixed frequency. We assume that the obstacle is either a perfect conductor coated by a thin dielectric layer or a dielectric coated by a thin layer of a highly conducting material, i.e., the coated portion of the boundary is modeled by either an impedance boundary condition or a conductive boundary condition. No a priori assumption is made on the connectivity of the scattering obstacle nor on the extent of the coating, i.e., the object can be fully coated, partially coated, or not coated at all. We present an algorithm based on the linear sampling method for reconstructing the shape of the scattering obstacle together with an estimate of either the surface impedance or surface conductivity. Numerous numerical examples are given showing the efficaciousness of our method. [ABSTRACT FROM AUTHOR]

We consider the problem of reconstructing the shape of perfectly conducting cylinders under the physical optics approximation. For direct scattering, physical optics provides small model errors when the scatterers are convex, smooth, have large radii of curvature as compared to the impinging wavelength, and ai are noninteracting. In this paper, we investigate whether these hypotheses can be relaxed for the inverse problem. In particular, we we consider three classes of scatterers (circular cylinder with radius smaller than the wavelength, multiple cylinders, and a concave cylinder) and we show that for them the model error is provided by a multiplicative almost frequency-independent factor. Since this factor can be incorporated within the unknown distribution representing the scatterers' illuminated boundaries, then we are able to show that successful reconstructions also beyond the physical optics limits can be obtained. [ABSTRACT FROM AUTHOR]

In clearing terrains contaminated or potentially contaminated by landmines and/or unexploded ordnances (UXOs), a quick wide-area surveillance is often required. Nevertheless, the identification of dangerous areas (instead of the detection of each subsurface object) can be enough for some scenarios/applications, allowing a suitable level of security in a cost-saving way. In such a framework, this paper describes a probabilistic approach for the definition of risk maps. Starting from the measurement of the scattered electromagnetic field, the probability of occurrence of dangerous targets in an investigated subsurface area is determined through a suitably defined classifier based on a support vector machine. To assess the effectiveness of the proposed approach and to evaluate its robustness, selected numerical results related to a two-dimensional geometry are presented. [ABSTRACT FROM AUTHOR]

A generalized technique for the reconstruction of permittivity profiles in an arbitrary coordinate system is presented. The resolution of the reconstructed permittivity profile can precisely be controlled by adjusting the ratio between the bandwidth and the midband frequency of frequency-dependent measured data, or equivalently the duration of a pulse modulated carrier used to produce time-dependent measurements. The proposed technique represents in fact a versatile relaxation of the well-known Fourier transformation method used to reconstruct one-dimensional profiles in half-spaces or slab-shaped media in Cartesian coordinate systems. Representative cases in the Cartesian coordinate system have been considered for validating the suggested technique. Excellent agreement between the original and reconstructed permittivity profiles has been achieved. [ABSTRACT FROM AUTHOR]

Summary: In this paper, by applying a non linear model for the electromagnetic inverse scattering, a technique for the dielectric profiling of a planarly layered medium is investigated and applied to void localization and diagnostics inside a homogeneous lossless slab (one-dimensional geometry). Data are collected under plane wave multifrequency normal incidence. Suitable finite dimensional representations for the unknown functions are introduced and their influence on the model is discussed. The resulting functional equation is solved by the method of weighted residuals and the solution algorithm amounts to minimizing a non quadratic function, where particular attention is devoted to reduce the occurrence of local minima. Finally, the inversion algorithm is validated by applications to both simulated and experimental data. [Copyright &y& Elsevier]

A novel method for the reconstruction of inhomogeneous permitivity profiles of spherical dielectric objects illuminated by higher order TEmn and TMmn spherical modes is presented. The overall technique is based on the derivation of Riccati-similar nonlinear differential equations in a spherical coordinate system for both TE and TM illuminations as a part of the direct problem formulation. These differential equations are then inverted using a quasi-linear approach to obtain a closed-form expression of the radially varying permitivity profile of spherical objects in terms of a spherical Fourier-Bessel transform of the measured spectral domain reflection coefficient data. To validate the proposed method, several examples with different mode illuminations and with different noise levels are considered for reconstructions. A good agreement between the actual and the reconstructed perceptivity profiles even under high noisy conditions shows that our method is not much sensitive to the presence of noise in the reflection coefficient data. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the reconstruction of the shape of unknown perfectly conducting objects from the knowledge of the scattered electric far field in a two-dimensional geometry. By adopting the Kirchhoff approximation, the problem is cast as a linear inverse one and is solved by resorting to the Singular Value Decomposition (SVD) approach. The finiteness of the available data along with the presence of the noise make undesired features on the reconstructed image arise. We here give some criteria for the choice of a threshold to cut them out from the reconstructions. Furthermore, we illustrate the processing of multi-view data. [Copyright &y& Elsevier]

The second version of the "linear sampling" method is considered with reference to perfectly conducting cylinders and its performances analyzed. It is pointed out that, for nonconvex objects, the shape of the object under test is not retrieved, whereas in its place the convex hull is recovered . We also point out that in the case of aspect limited data neither the convex hull of the object is reconstructed. [ABSTRACT FROM AUTHOR]