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A noniterative and efficient method is developed to recover refractive index of a medium which is a function of only two spatial variables from the information on forward scattering amplitude for electromagnetic plane waves incident at different angles and frequencies. To test implementation feasibility of the proposed method and its performance, some preliminary numerical calculations are presented. [ABSTRACT FROM AUTHOR]

This work presents a 2‐step Learning‐by‐Examples approach for the real‐time classification of hemorrhagic/ischemic brain strokes and their successive localization from microwave scattering data collected around the human head. An experimental assessment against laboratory‐controlled data is performed to assess the potentialities of the proposed approach towards a reliable monitoring and instantaneous diagnosis clinic protocol. [ABSTRACT FROM AUTHOR]

This letter proposes a diagonalized improved subspace-based optimization method (DISOM) by introducing the diagonal approximation to the improved subspace-based optimization method (ISOM). In the diagonal approximation which has been used in the contrast source inversion, a diagonal operator is used to replace the nonlinear operator of full contrast inversion and relates the fields and induced currents. Due to the diagonal approximation, a more simplified objective function is obtained. Consequently, the iteration procedure is simplified and the computation time is reduced. Numerical examples demonstrate that the proposed DISOM has the capability of reconstructing not only isotropic objects but also uniaxial anisotropic objects. Furthermore, the quality of the reconstruction results obtained by DISOM is almost the same as the ones by utilizing ISOM, while DISOM saves about one fourth of the computational time. [ABSTRACT FROM AUTHOR]

ABSTRACT An inverse scattering approach using only total electric field data is developed for reconstructing electrical parameters of unknown scatterers. Two interior boundary value problems are set up whose solutions coincide with each other if and only if a medium inside the observation surface is the same as that of the original scattering problem. A cost functional of misfit between the two solutions is introduced to solve the inverse problem and its gradient is derived explicitly. Numerical examples are provided to assess the proposed inversion approach. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:137-141, 2015 [ABSTRACT FROM AUTHOR]

In the framework of the multitask Bayesian compressive sensing (BCS) paradigm, two innovative approaches for the solution of coherent imaging problems are proposed within the first-order Born approximation and the Rytov approximation.Selected numerical results are reported to compare the proposed techniques with state-of-the-art BCS approaches as well as global optimization-based methods. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:1553-1558, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27612 [ABSTRACT FROM AUTHOR]

The inversion method developed by Reese T. Prosser for waves in three dimensions is modified to solve inverse problems of back scattered data for TM plane waves incident on cylindrical structures with dielectric properties that are function of two spatial variables. Not only the bounds needed for convergence proof of the modified method are found but also the method is numerically implemented and its numerical performance examined. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:561-566, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27383 [ABSTRACT FROM AUTHOR]

A Newton-based Hybrid method for reconstruction of the shape of dielectric objects through the measured far-field scattering data is given. The scattered field is represented as a single-layer potential which leads to an ill-posed integral equation of the first kind that is solved via Tikhonov regularization. The presented Newton-based method combines ideas of both the iterative and decomposition methods and inherits the advantages of each of them, such as getting good reconstructions and not requiring a forward solver at each step. The numerical results show that the method yields good reconstruction. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1147–1151, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24218 [ABSTRACT FROM AUTHOR]

In this article, a hybrid method is presented to reconstruct two-dimensional shape of an inhomogeneous impedance cylinder from the noisy far field data in the case of single electromagnetic plane wave illumination. The proposed reconstruction method can also be applied for complex-shaped smooth objects having different type of boundary conditions. For the solution of the direct problem, a potential (layer) approach is chosen that leads to a boundary integral equation. Applying Nyström method to the equation, an exponential convergence is obtained. The inverse scattering problem is solved via neural network approach, which is a stable technique under considerable level of noise. The applicability and the effectiveness of the proposed method are supported by numerical examples, and the proposed approach provides reconstructions which are in good agreement with the actual shapes. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 119–124, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23953 [ABSTRACT FROM AUTHOR]

A genetic programming-based geometry optimization method for inverse scattering that uses a tree data structure to encode Boolean combinations of convex shapes has recently been shown to outperform other genetic algorithm-based techniques. Nonetheless, the genetic algorithms are still inefficient for inverse scattering. This letter treats the inefficiency with local search techniques. First, an implementation using greedy search is discussed. Next, a local search method is added to the genetic algorithm used in the previous approach. Numerical results show that the number of function evaluations necessary to image conducting cylinders can be reduced by several orders of magnitude. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 822–825, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23222 [ABSTRACT FROM AUTHOR]

In this article, we present a new hybrid method to reconstruct one-dimensional lossy profile in order to get effective and stable solutions that can be used for both acoustic and electromagnetic cases. Unlike classical integral equation methods for the solution of the inverse medium problems, the neural network approach is applied to avoid the nonlinear and ill-posed nature of the integral equation of the first kind. The applicability and the effectiveness of the method is tested by selecting an inverse problem, namely, to determine nonsmooth one-dimensional profile of an inhomogeneous layer located over an inhomogeneous impedance ground. To reveal the advantage and the accuracy of the method, noisy data and rectangular/triangular types of non-smooth profiles are used. Good agreement with exact profiles has been observed. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 3158–3162, 2007; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.22958 [ABSTRACT FROM AUTHOR]

An analytical approach to inverse electromagnetic scattering is proposed. A two-dimensional geometry is considered. A closed-form singular value decomposition of the scattering integral operator is derived and is used to reconstruct the radiating components of the equivalent current density. This is the first step toward a more complete solution that will account for the nonradiating currents, too, and will be used to compute the dielectric features of the body under test. Numerical simulations show the capabilities of the method to reconstruct the radiating current. The model resolution kernel of the scattering operator can be also easily derived. By virtue of the closed-form solution, results can be achieved in a very short computational time. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 354–360, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22125 [ABSTRACT FROM AUTHOR]

In this paper, a new method for the solution of inverse scattering by dielectric circular cylinder is proposed. The original problem is recast into a regression estimate one by means of a regression technique based on the use of support vector machine. The proposed method, after a proper training procedure, is able to reconstruct the unknown dielectric objects and their dielectric permittivities inside a given investigation domain. Numerical results show the accuracy and efficiency of the approach. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 372–375, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22131 [ABSTRACT FROM AUTHOR]

We have proposed a time-domain forward-backward time-stepping (FBTS) method for reconstructing 3D structures in highly absorptive media. The reconstruction speed is greatly dependent on the number of transmitters. In this paper, we propose a source-group method to speed up the reconstruction. In the source-group method, multiple transmitters arranged at different positions are excited simultaneously, and receivers collect the wave fields. To compare the reconstruction results, three kinds of reconstructions from 16 conventional single transmitter-multiple receiver data sets, four source-group multiple-receiver data sets, and four conventional single-transmitter multiple-receiver data sets are carried out. Reconstruction by the source-group method is several times faster than (and the reconstructed results are almost the same as) those of the first kind of reconstruction, and they are much better than those of the third kind. © Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 67–71, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21263 [ABSTRACT FROM AUTHOR]

In this paper, with reference to limited-angle data configurations, the performance of the nonlinear multiscaling inversion approach (IMSA) is analyzed. Such an assessment is carried out by considering synthetically generated as well as laboratory-controlled experimental data (“Marseille data”) concerning 2D dielectric scatterers. The obtained results demonstrate a satisfactory robustness and the reliability of the approach. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 358–363, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20634 [ABSTRACT FROM AUTHOR]

An iterative time-domain algorithm for reconstructing three-dimensional (3D) lossy objects using microwave data transmitted and collected by dipole antennas is presented. The electromagnetic and adjoint fields are calculated using the finite-difference time-domain (FDTD) method. Numerical examples show the algorithm can rebuild simultaneously from noise-free and noisy data the permittivity and conductivity of a 3D lossy object settled in a lossless background. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 238–243, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20598 [ABSTRACT FROM AUTHOR]

This paper addresses the problem of reconstructing homogeneous cylinders buried in a known soil, starting from the electromagnetic data collected by a subsurface radar moving on the soil surface. The proposed approach makes use of neural networks to process some data extracted from the electromagnetic time responses of the subsoil. Some numerical results are given concerning a single cylinder of circular shape. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 353–357, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20303 [ABSTRACT FROM AUTHOR]

An adaptive nonlinear inversion method based on the Riccati equation in the dispersive inverse-scattering problem is presented for synthesizing both single and coupled nonuniform transmission lines (NTLs) with arbitrary lobe-like backward responses. In this method, the specified responses of those lines are first shaped by an optimum perturbation of inherent null points in the electrical-length domain, and then sampled to straightforwardly determine the corresponding modal impedance profiles, hence avoiding the step-by-step segmentation process and overall optimization routines that plague most inversion schemes supporting non-TEM modes. Some transformers and filters with controlled responses are illustrated for generality. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 52–56, 2003 [ABSTRACT FROM AUTHOR]

This paper discusses a special imaging reconstruction problem in which the object to be reconstructed resides in a homogeneous media but consists of a known part and an unknown part. The known part is combined with the homogeneous background media to form an inhomogeneous media. The dielectric permittivity profiles are reconstructed for the unknown part using the Born iteration (BI) method. Numerical examples demonstrate that this modified BI algorithm has faster convergence and higher accuracy than the regular BI method. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 91–95, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10684 [ABSTRACT FROM AUTHOR]

A new design method for a tapered impedance-matching line is proposed. The accurate characteristic impedance profile of the desired matching line is obtained through the accurate profile inversion of a virtual dielectric medium which is equivalent to the matching line in view of the reflection characteristic. Then, the matching line is synthesized according to the characteristic impedance profile. The method can be applied to design impedance-matching lines with arbitrary passband characteristics without any equivalent-circuit analysis. In this method, the inevitable errors in the method using the time-domain reflection coefficient can be avoided by using the frequency-domain reflection coefficient. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 393–396, 2002. [ABSTRACT FROM AUTHOR]

The reconstruction of the parameters of underground targets is still highly anticipated in ground-penetrating radar (GPR) applications. In this paper, the FDTD method and time-domain optimization algorithm are used to reconstruct the permittivities of underground multiple targets. An iterative optimization algorithm is proposed. The forward scattering data are also calculated by a 2.5-D–FDTD algorithm in order to better simulate the practical GPR situation. The relationship between the convergence rates of the inverse algorithm and the initialization values are studied. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 384–387, 2001. [ABSTRACT FROM AUTHOR]

A novel reconstruction method of a one-dimensional medium from information contained in the frequency-domain reflection coefficient is considered. An approximate formula produced by applying a fractional linear transformation (FLT) to the nonlinear Riccati differential equation is used. The phase compensation constant (PCC) is introduced in order to reduce the phase error of the reconstructed permittivity profile of a discontinuous medium. Finally, the effective error reduction in the reconstructed profiles is shown by examples, which demonstrate the validity of this method. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 10–13, 2001. [ABSTRACT FROM AUTHOR]

Electromagnetic inverse scattering of a perfectly conducting cylinder with real data by using the real-coded genetic algorithm is presented in this paper. The cylinder is denoted by a local shape function with respect to its local origin. The inverse problem is to locate the cylinder, and to reconstruct its shape given the measured scattered electric field. To guarantee the nonnegative definiteness of the local shape function, it is approximated as cubic B-splines with N control points instead of a trigonometric series of order N/2. The local origin and the control points are the optimization parameters for the real-coded genetic algorithm. They are searched in a very wide space. A sample rectangular cylinder which is center located or decenter located is reconstructed. The reconstruction results confirm the strong search ability and the robustness of the real-coded genetic algorithm. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 315–320, 2001. [ABSTRACT FROM AUTHOR]

A new iterative algorithm for the reconstruction of two-dimensional lossless objects is developed using time-domain scattering data. All of the calculations in both the forward and inversion algorithms are carried out efficiently in the time domain using the finite-difference time-domain (FDTD) method. Computer simulations are presented to illustrate the usefulness of the present method. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 72–77, 1999. [ABSTRACT FROM AUTHOR]

A computational method combining the genetic algorithm (GA) and shape mutation is reported for electromagnetic imaging of a homogeneous cylinder of arbitrary shape. By measuring the scattered field, the shape location, size, and permittivity of the object are retrieved quite successfully. The forward problem is solved based on the equivalent source current and the method of moments (MoM), while the inverse problem is reformulated into an optimization one, and is solved by the proposed scheme. Numerical simulation shows that, even with a bad initial guess, good reconstruction can be obtained for a hollow object or multiple-cylinder object as long as the noise level is ≤-20 dB. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 188–192, 1998. [ABSTRACT FROM AUTHOR]

In this letter, a new method for reconstructing the bound of impenetrable two-dimensional objects is presented. From a set of measurements in the near- or far-field region, we calculate the coefficients of multipolar equivalent sources located inside the unknown object. Thus, the shape of the object is obtained through the constraint of the tangential electric field boundary condition. Numerical simulations for TM polarization problems are presented to demonstrate the accuracy of the proposed method. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 18: 429–432, 1998. [ABSTRACT FROM AUTHOR]

A numerical method using matrix inversion has been generalized to solve the Gel'fand–Levitan–Marchenko (GLM) inverse scattering problem for arbitrary forms of reflection coefficient data for plasma medium. An accurate representation of the reflection transient was calculated using the Gauss–Legendre method with a small number of sampling data points of the reflection coefficient. The reflection coefficient has also been derived in a closed form for a uniform plasma layer, and the inversion result accurately reconstructed the original profile. The algorithm can also be applied to reconstruct the 1-D profile for inhomogeneous plasma medium from measured reflection coefficient data. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 17: 97–101, 1998. [ABSTRACT FROM AUTHOR]

In this article we present a modified version of the time-domain distorted Born iterative method (TDDBIM), based on the frequency-compensating technique (FCT), for the reconstruction of lossy dielectric objects. The FCT is applied to improve the ill-posed characteristics of the inverse problems and to speed up the convergence of the TDDBIM. Numerical results for the reconstruction of two-dimensional lossy objects show that the algorithm is very effective in improving the rate of convergence of the TDDBIM. Furthermore, the modified algorithm performs well even in the presence of a 20-dB signal-to-noise ratio and does not impose an additional burden on the CPU. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 15: 282–288, 1997 [ABSTRACT FROM AUTHOR]

An approach to three-dimensional microwave imaging is proposed. Usually, because of the wide computational resource that is required by this kind of imaging that is based on the full-vector integral equations for the inverse scattering problem, linearizing approximations are employed. In this Letter, we exploit the use of the Rayleigh approximation in conjunction with a previously proposed numerical solution. We will show that the approach requires the same computational load as the one that makes use of the first-order Born approximation, but it provides an improvement in the reconstruction accuracy for a certain range of contrast values. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 15: 173–176, 1997. [ABSTRACT FROM AUTHOR]

The inverse scattering of dielectric cylinders buried in a half space is investigated. Dielectric cylinders of unknown permittivities are buried in one half space and scatter a group of unrelated waves incident from another half space where the scattered field is recorded. By proper arrangement of the various unrelated incident fields, the difficulties of ill-posedness and nonlinearity are circumvented, and the permittivity distribution can be reconstructed through simple matrix operations. The algorithm is based on the moment method and the unrelated illumination method. Numerical results show that good reconstruction has been obtained both with and without Gaussian noise in measured data. [ABSTRACT FROM AUTHOR]

Some procedures for the regularization of inverse-scattering problems are evaluated and discussed by using a singular value decomposition of the Green operator. Results of numerical simulations of a cylindrical scatterer are reported to show the limitations and the capabilities of the described methods. [ABSTRACT FROM AUTHOR]

The inverse scattering of inhomogeneous biaxial dielectric cylinders is investigated. Assume that an incident wave is incident upon anisotropic cylinders of unknown dielectric constant distribution, and the scattered field is measured outside. By properly processing the scattered field, the dielectric-constant distribution of the object can be reconstructed. For the theoretical formulation, based on the proper arrangement of the direction and polarization of the incident field, a set of integral equations that can be solved by the moment method and an unrelated illumination method is derived. Numerical results are given to demonstrate the capability of the inverse algorithm. Good reconstruction is obtained even in the presence of additive random noise in measured data. In addition, the effect of noise in the reconstruction result is also investigated. [ABSTRACT FROM AUTHOR]

This article introduces a numerical technique for solving the inverse problem in dispersive scattering theory. The inverse problem is first formulated as a relationship between the impulse response R and the susceptibility kernel G. Using the Legendre-Gauss-Lobatto nodes we construct the Nth polynomial interpolation to approximate the solution of G for a given R. This method is efficient and yields very accurate results. Illustrative examples are included to demonstrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

A new integral-equation-based numerical approach to microwave imaging is presented. It can be applied to focused imaging in the sense that only one part of an inhomogeneous body is viewed as an unknown scatterer to be reconstructed. This approach is of great usefulness in many applications, as it results in a notable computational saving and in high flexibility. Moreover, it allows the range of applicability of the Born approximation to be considerably expanded. [ABSTRACT FROM AUTHOR]

This article describes a technique to reduce the poor conditioning of linear systems to be solved for numerical inverse-scattering solutions based on integral formulations and on the moment method. Some preliminary results are reported to show the improvement over a previously proposed approach. [ABSTRACT FROM AUTHOR]

Microwave imaging for dielectric objects under the Born approximation is suggested by using the computerized tomography based on projection. Limiting factors of degradation in reconstructed images are identified and explored in terms of projection function and necessary condition on the first-order Born approximation. To illustrate the usefulness of the presented method, simulation and experiment are performed in this article. [ABSTRACT FROM AUTHOR]

A spectral inverse technique, applying the moment-method procedure with a series expansion for the induced field in each enlarged cell, is suggested to reconstruct permittivity profiles of inhomogeneous dielectric objects. In particular, averaging the reconstructed permittivity distribution over each cell with a weighting function becomes an effective tool to regularize the error arising from a Gaussian random noise of the scattered field. [ABSTRACT FROM AUTHOR]

The genetic algorithm is combined with a moment method solver to carry out the shape inversion of two-dimensional metallic objects. The binary bitmap discretization is used in conjunction with geometrical median filtering to describe the shape of the object. Results of the shape inversion with the use of this algorithm are presented for several Ipswich objects based on measurement data. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 457–459, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10349 [ABSTRACT FROM AUTHOR]

A novel on-line inverse-scattering method for the geometric characterization of conducting cylindrical scatterers from scattered-field measurements is presented. The method is based on the application of radial basis-function neural networks that are constructed by use of the orthogonal least squares algorithm. Thus, trial-and-error approaches during the construction can be avoided. The efficiency and robustness of the method in inverting noisy measurements are investigated. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 378–380, 2001. [ABSTRACT FROM AUTHOR]

A neural-network approach is developed to investigate the inverse scattering from a perfectly conducting circular cylinder due to a normal field incidence. The neural network, is used to predict the electrical radius ka of a circular cylinder by recovering the complex coefficients of the cylindrical wave expansion of the scattered field. The neural network, therefore, is trained to model the nonlinear relation between the electrical radius and the numerical values of the complex expansion coefficients of the far field. [ABSTRACT FROM AUTHOR]

The potential profile of the one-dimensional Schrödinger equation may be inverted from the reflection coefficient. For example, the famous Gel'fand-Levitan equation shows their relation. But, in the general case, GL equation may hardly be solved exactly. Based on the Hulthén-Kohn variational method for calculating the reflection coefficient, a closed-form approximation formulation is used in this Letter for inverting the potential profile. Inversion examples show that this formulation works better than the famous modified Born approximation. [ABSTRACT FROM AUTHOR]

The conductivity profile in version for purely conducting media is studied Presently, some approximation inversion formulations are given for this problem, In this Letter, a generalized Gel'fand-Lavitan equation is given for exact inversion. Like the famous GL equation, the generalized GL equation is exactly solvable when the reflection coefficient is a rational function. Reconstruction examples are also given. [ABSTRACT FROM AUTHOR]

For a half-space barrier potential, it has been shown that the potential functions in a shallow region 0 < x < d can be accurately reconstructed by using a generalized Born approximation from the reflection coefficient r(k) at x = 0, and the reconstructed error is notable when x > d. By using the network theory presented in this article, we can transform the reflection coefficient at x = 0 into the one at x = d, from which the potential functions of the region x > d can be accurately reconstructed. Numerical examples are given, which show the applicability of this method. [ABSTRACT FROM AUTHOR]

Formulation in cylindrical coordinates for the reconstruction of the permittivity profiles using the moment method is presented. Angular spectral domain reconstruction is shown to be less sensitive to the ill-posedness due to the noise in the scattered field than the configuration-domain reconstruction. [ABSTRACT FROM AUTHOR]

In this article a numerical method that makes use of matrix inversion to solve the Gel'fand–Levitan–Marchenko (GLM) integral equation for electromagnetic inverse scattering is presented. The algorithm is validated by comparing it to the analytic solution of the inverse problem for the reflection coefficient with a rational function. This approach can be applied to a GLM inverse scattering problem with a general reflection coefficient or experiment data, for which an analytic solution of the GLM integral equation is not available. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 15: 277–278, 1997. [ABSTRACT FROM AUTHOR]