This study proposes a low-complexity permittivity estimation for ground penetrating radar applications based on a contrast source inversion (CSI) approach, assuming multilayered ground media. The homogeneity assumption for each background layer is used to address the ill-posed condition while maintaining accuracy for permittivity reconstruction, significantly reducing the number of unknowns. Using an appropriate initial guess for each layer, the post-CSI approach also provides the dielectric profile of a buried object. The finite difference time domain numerical tests show that the proposed approach significantly enhances reconstruction accuracy for buried objects compared with the traditional CSI approach.

A method to reconstruct the surface shape of a scatterer from the relative intensity of the scattered field is proposed. Reconstruction of the scatterer shape has been studied as an inverse problem. An approach that employs boundary-integral equations can determine the scatterer shape with low computation resources and high accuracy. In this method, the reconstruction process is performed so that the error between the measured far field of the sample and the computed far field of the estimated scatterer shape is minimized. The amplitude of the incident wave at the sample is required to compute the scattered field of the estimated shape. However, measurement of the incident wave at the sample (measurement without the sample) is inconvenient, particularly when the output power of the wave source is temporally unstable. In this study, we improve the reconstruction method with boundary-integral equations for practical use and expandability to various types of samples. First, we propose new boundary-integral equations that can reconstruct the sample shape from the relative intensity at a finite distance. The relative intensity is independent from the amplitude of the incident wave, and the reconstruction process can be performed without measuring the incident field. Second, the boundary integral equation for reconstruction is discretized with boundary elements. The boundary elements can flexibly discretize various shapes of samples, and this approach can be applied to various inverse scattering problems. In this paper, we present a few reconstruction processes in numerical simulations. Then, we discuss the reason for slow-convergence conditions and introduce a weighting coefficient to accelerate the convergence. The weighting coefficient depends on the distance between the sample and the observation points. Finally, we derive a formula to obtain an optimum weighting coefficient so that we can reconstruct the surface shape of a scatterer at various distances of the observation points.

We propose a new swept-frequency measurement method for the electromagnetic characterization of materials. The material is a multilayer cylinder that pierces a rectangular waveguide through two holes in the narrow waveguide walls. The complex permittivity and permeability of the material are calculated from measured S-parameters as an inverse problem. To this aim, the paper develops a complete electromagnetic formulation of the problem, where the effects of material insertion holes are taken into consideration. The formulation is validated through the measurement of ferrite and water samples in the S-band.

Microwave ultra-wideband (UWB) radar systems are advantageous for their high-range resolution and ability to penetrate dielectric objects. Internal imaging of dielectric objects by UWB radar is a promising nondestructive method of testing aging roads and bridges and a noninvasive technique for human body examination. For these applications, we have already developed an accurate internal imaging approach based on the range points migration (RPM) method, combined with a method that efficiently estimates the dielectric constant. Although this approach accurately extracts the internal boundary, it is applicable only to highly conductive targets immersed in homogeneous dielectric media. It is not suitable for multi-layered dielectric structures such as human tissues or concrete objects. To remedy this limitation, we here propose a novel dielectric constant and boundary extraction method for double-layered materials. This new approach, which simply extends the Envelope method to boundary extraction of the inner layer, is evaluated in finite difference time domain (FDTD)-based simulations and laboratory experiments, assuming a double-layered concrete cylinder. These tests demonstrate that our proposed method accurately and simultaneously estimates the dielectric constants of both media and the layer boundaries.

An algorithm is formulated for reconstructing a dielectric cylinder with the use of the T-matrix and the singular value decomposition (SVD) and is discussed through numerical examples under noisy conditions. The algorithm consists of two stages. At the first stage the measured data of scattered waves is transformed into the T-matrix. At the second stage we reconstruct the cylinder from the T-matrix. The singular value decomposition is applied in order to separate the radiating and the nonradiating currents, and the radiating current is directly obtained from the T-matrix. The nonradiating current and the object are reconstructed by decreasing a residual error of the current in the least square approximation, where linear equations are solved repeatedly. Some techniques are used in order to reduce the calculation time and to reduce the effects of noise. Numerical examples show us that the presented approach is simple and numerically feasible, and enables us to reconstruct a large object in a short time.

An inverse scattering problem of estimating the reflection coefficient and the surface impedance from two sets of absolute values of the near field with periodic change is investigated. The problem is formulated in terms of a nonlinear simultaneous equations which is derived from the relation between the two sets of absolute values and the field defined by a finite summation of the modal functions by applying the Fourier analysis. The reflection coefficient is estimated by solving the equations by Newton's method through the successive algorithm with the increment of the number of truncation in the summation one after another. Numerical examples are given and the accuracy of the estimation is discussed.

An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.

An inverse scattering problem of estimating the surface impedance for an inhomogeneous half-space is investigated. By virtue of the fact that the far field representation contains the spectral function of the scattered field, complex values of the function are estimated from a set of absolute values of the far field. An approximate function for the spectral function is reconstructed from the estimated complex values by the least-squares sense. The surface impedance is estimated through calculating the field on the surface of the half-space expressed by the inverse Fourier transform. Numerical examples are given and the accuracy of the estimation is discussed.

Target reconstruction algorithm from its monostatic radar cross section (RCS) has been proposed for polygonal cylinders with curved surfaces. This algorithm is based on our previous finding that the main contribution to the back scattering is due to edge diffracted fields excited at a facet of nearly specular reflection direction. Dimension of this constitutive facet of the target is estimated from the local maxima and its lobe width in the angular RCS variation. Half and quarter circular cylinders are used as canonical scattering objects, and their measured and numerically simulated monostatic RCS values have been studied extensively to find scattering pattern characteristic difference between flat and circularly curved surfaces. Thus estimated constitutive facets are connected in order, and this procedure will be continued until the distance between the first and the final edges would be minimized. Our algorithm has been tested for other targets, and it is found that it works well for predicting metal convex targets with flat and curved facets.

An electromagnetic (EM) inverse scattering problem that involves the reconstruction of microwave images for dielectric objects is considered in this paper. This ill-posed and nonlinear problem is treated as a global optimization problem, and is solved by the application of micro-genetic algorithm (m-GA). The reconstructed results obtained by m-GA have shown that it is an effective technique for microwave imaging and satisfactory performance is achieved when compared with the conventional genetic algorithms.

In this paper, genetic algorithms is employed to determine the shape of a conducting cylinder buried in a half-space. Assume that a conducting cylinder of unknown shape is buried in one half-space and scatters the field incident from another half-space where the scattered filed is measured. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. The genetic algorithm is then employed to find out the nearly global extreme solution of the object function such that the shape of the conducting scatterer can be suitably reconstructed. In our study, even when the initial guess is far away from the exact one, the genetic algorithm can avoid the local extremes and converge to a reasonably good solution. In such cases, the gradient-based methods often get stuck in local extremes. Numerical results are presented and good reconstruction is obtained both with and without the additive Gaussian noise.

This paper presents a fast inversion method for electromagnetic imaging of cylindrical dielectric objects with the optimal regularization parameter used in the Levenberg-Marquardt method. A novel procedure for choosing the optimal regularization parameter is proposed. The method of moments with pulse-basis functions and point matching is applied to discretize the equations for the scattered electric field and the total electric field inside the object. Then the inverse scattering problem is reduced to solving the matrix equation for the unknown expansion coefficients of a contrast function, which is represented as a function of the relative permittivity of the object. The matrix equation may be solved in the least-squares sense with the Levenberg-Marquardt method. Thus the contrast function can be reconstructed by the minimization of a functional, which is expressed as the sum of a standard error term on the scattered electric field and an additional regularization term. While a regularization parameter is usually chosen according to the generalized cross-validation (GCV) method, the optimal one is now determined by minimizing the absolute value of the radius of curvature of the GCV function. This scheme is quite different from the GCV method. Numerical results are presented for a circular cylinder and a stratified circular cylinder consisting of two concentric homogeneous layers. The convergence behaviors of the proposed method and the GCV method are compared with each other. It is confirmed from the numerical results that the proposed method provides successful reconstructions with the property of much faster convergence than the conventional GCV method.

The genetic algorithm is used to reconstruct the shapes of multiple perfectly conducting cylinders. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. The genetic algorithm is then employed to find out the global extreme solution of the object function. Numerical examples are given to demonstrate the capability of the inverse algorithm. Good reconstruction is obtained even when the multiple scattering between two conductors is serious. In addition, the effect of Gaussian noise on the reconstruction results is investigated.

A signal processing approach is discussed which has the potential for imaging strongly scattering objects from a series of scattering experiments. The method is based on a linear spectral estimation technique to replace the filtered backpropagation for limited discrete data and a subsequent nonlinear signal processing step to remove the contribution of multiple scattering my means of homomorphic filtering. Details of this approach are discussed and illustrated by applying the imaging algorithm to both simulated and real data.

An inverse scattering problem in three dimensional two layered media is investigated. The shape and the location of the acoustic scatterer buried in one half-space are determined. With some a priori information, it becomes possible to solve this problem in three dimensions. Using the moment method, the scattered field is obtained for the estimated scatterer. An iterative procedure based on the Newton's method for the nonlinear least square problem is able to solve the inverse scattering problem. Some numerical results are presented.

A two-dimensional algorithm, which combines the well-known Synthetic Aperture Radar (SAR) imaging and the recently developed effective inversion method, is presented and applied to a three-dimensional configuration. During the first stage a two-dimensional image of a realistic three-dimensional buried object is obtained. In the second stage the average permittivity of the object is estimated using a two-dimensional effective inversion scheme where the geometrical information retrieved from the SAR image is employed. The algorithm is applicable in real time.

A novel technique is developed to reconstruct a nonuniform transmission line by using arbitrary incident waveforms. By discretizing both the incident and reflected waves, we find that the ratio of reflected wave to incident wave has the same form as the reflection coefficient obtained by treating a nonuniform line as a cascaded, multiple-section signal line. A reconstruction scheme is derived to get the impedance profile of a nonuniform line. Some examples are presented to illustrate this new technique.

In this paper, we analyze the inverse scattering problem by a new deterministic method called "Source and Radiation Field Solution," which has the merit that both the source and the radiation field can be treated at the same time, the effect of which has already shown in ordinary scattering problems.

A method is presented for reconstructing the surface profile of a two dimensional rough surface boundary from the scattered far field data. The proposed inversion algorithm is based on the Kirchhoff approximation and in order to determine the surface profile, the numerical results illustrating the method are presented.

We present a novel algorithm to reconstruct the refractive-index profile of a circularly symmetric object from measurements of the electromagnetic field scattered when the object is illuminated by a plane wave. The reconstruction algorithm is besed on an iterative procedure of matching the scattered field calculated from a certain refractive-index distribution with the measured scattered field on the boundary of the object. In order to estimate the convergence of the reconstruction, the mean square error between the calculated and measured scattered fields is introduced. It is shown through reconstructing several examples of lossy dielectric cylinders that the algorithm is quite stable and is applicable to high-contrasty models in situations where the Born approximation is not valid.