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In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work. [ABSTRACT FROM AUTHOR]

A hybrid method which is suitable to find numerical solutions for two-dimensional inverse scattering problems connected with cylindrical bodies buried in a half-space with the known orientation is established. The mentioned hybrid method is based on the classical moment method in connection with vertical coordinate while it involves the horizontal coordinate through a spectral expansion. The structure of the spectral expansion which is imposed by the Green's function contributes to improvement of the ill-posedness of the problem along with Tikhonov regularization. By taking this particular structure into consideration one determines the basis functions such that the effect of the ill-posedness is reduced to a minimum. Someillustrative examples show the applicability and accuracy of the method. [ABSTRACT FROM AUTHOR]

We define a reciprocity gap functional for electromagnetic scattering in chiral media. We assume that a perfectly conducting scatterer is embedded in a piecewise homogeneous isotropic background chiral medium. The incident field is a spherical electromagnetic wave due to a point source located at a point contained in a chiral environment. We also define the chiral reciprocity gap operator and we prove that it is injective and it has dense range. Using these results and appropriate density properties of chiral Herglotz functions we solve an inverse scattering problem for the determination of the boundary of the scatterer from the knowledge of the tangential components of the electric and magnetic fields. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm to reconstruct one-dimensional impenetrable rough surface from the knowledge of scattering field is presented. The rough surface is considered as locally perturbed and the scattering field data are collected above the roughness in a simple non-magnetic medium considering Neumann boundary condition. First, the surface integral equation constituted via the Neumann boundary condition is solved and scattering field data are observed synthetically. Then, the same surface integral equation together with the data equation are solved in an iterative fashion to reconstruct the surface variation. In the numerical implementation, the so-called ill-posed inverse problem is regularized with Tikhonov method and a least-squares solution is obtained by using Gaussian-type basis function. Finally, numerical examples are carried out to illustrate effectiveness of the method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from near field scattering data. This method provides a fast numerical algorithm as well as a unique determination for the shape reconstruction of the scatterer. We present a rigorous justification and numerical examples for the factorization method. The transmission eigenvalue problem in scattering have recently attracted a lot of attentions. Transmission eigenvalues can be determined from scattering data and they can provide information about the material parameters of the scatterers. In this paper, we formulate the interior transmission eigenvalue problem and prove the existence of infinitely many transmission eigenvalues for the scattering from anisotropic periodic layers. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single direction of the incident plane wave. We propose a globally convergent convexification numerical algorithm to solve this nonlinear and ill-posed inverse problem. The key advantage of our method over conventional optimization approaches is that it does not require a good first guess about the solution. First, we eliminate the coefficient from the Helmholtz equation using a change of variables. Next, using a truncated expansion with respect to a special Fourier basis, we approximately reformulate the inverse problem as a system of quasilinear elliptic PDEs, which can be numerically solved by a weighted quasi-reversibility approach. The cost functional for the weighted quasi-reversibility method is constructed as a Tikhonov-like functional that involves a Carleman Weight Function. Our numerical study shows that, using a version of the gradient descent method, one can find the minimizer of this Tikhonov-like functional without any advanced a priori knowledge about it. [ABSTRACT FROM AUTHOR]

The inverse problem for the discrete analogue of the exterior transmission eigenvalue problem with a spherically symmetric index of refraction is considered. For the absorbing media, we show that the index of refraction can be recovered uniquely if all the exterior transmission eigenvalues (counting with their multiples) are given together with partial information on the entries of the index of refraction. Meanwhile, for the non-absorbing media, we obtain that exterior transmission eigenvalues can completely determine the index of refraction. [ABSTRACT FROM AUTHOR]

This paper presents an efficient implementation of the inversion algorithm based on the conjugate-gradient method (CGM) for solving inverse scattering problems. The original CGM provides good image reconstruction and robustness to noise-corrupted data. This method requires the solution of the forward scattering problem and the Fréchet derivative operator of the cost function at each iteration step. However, these procedures can make the computational cost prohibitive, even for moderately sized problems. To avoid the computational burden, a two-step conjugate gradient fast Fourier transform (CG-FFT) procedure is proposed. Such an approach reduces the computational cost and storage requirements of the CGM implementation. The efficient CGM is found to share a computational complexity similar to the distorted-Born iterative method (DBIM). Thus the convergence speed and accuracy of the CGM is compared with the DBIM. Numerical tests using both synthetic and experimental data show effectiveness for solving 2D inverse scattering problems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two transmission eigenvalue problems associated with the scattering of a media with a coated boundary. In recent years, there has been a lot of interest in studying these eigenvalue problems. It can be shown that the eigenvalues can be recovered from the scattering data and hold information about the material properties of the media one wishes to determine. Motivated by recent works we will study the electromagnetic transmission eigenvalue problem and scalar 'zero-index' transmission eigenvalue problem for a media with a coated boundary. Existence of infinitely many real eigenvalues will be proven as well as showing that the eigenvalues depend monotonically on the refractive index and boundary parameter. Numerical examples in two spatial dimensions are presented for the scalar 'zero-index' transmission eigenvalue problem. Also, in our investigation we prove that as the boundary parameter tends to zero and infinity we recover the classical eigenvalue problems. [ABSTRACT FROM AUTHOR]

The exterior transmission eigenvalue problem for anisotropic media with spherical symmetry assumptions is considered. First, we discuss the existence and the asymptotic distribution of exterior transmission eigenvalues. Then, we investigate the inverse problem of determining the index of refraction from a knowledge of two sets of spectral data under appropriate conditions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were first studied in Blåsten, E., Liu, H. (2017). On vanishing near corners of transmission eigenfunctions. J. Funct. Anal. 273(11):3616–3632. It is shown in two scenarios that the interior transmission eigenfunction must be locally vanishing near a corner of the domain with an interior angle less than π. We significantly extend and generalize those results in several aspects. First, we consider the conductive transmission eigenfunctions which include the interior transmission eigenfunctions as a special case. The geometric structures established for the conductive transmission eigenfunctions in this paper include the results in Blåsten, E., Liu, H. (2017). On vanishing near corners of transmission eigenfunctions. J. Funct. Anal. 273(11):3616–3632 as a special case. Second, the vanishing property of the conductive transmission eigenfunctions is established for any corner as long as its interior angle is not π when the conductive transmission eigenfunctions satisfy certain Herglotz functions approximation properties. That means, as long as the corner singularity is not degenerate, the vanishing property holds if the underlying conductive transmission eigenfunctions can be approximated by a sequence of Herglotz functions under mild approximation rates. Third, the regularity requirements on the interior transmission eigenfunctions in Blåsten, E., Liu, H. (2017). On vanishing near corners of transmission eigenfunctions. J. Funct. Anal. 273(11):3616–3632 are significantly relaxed in the present study for the conductive transmission eigenfunctions. In order to establish the geometric properties for the conductive transmission eigenfunctions, we develop technically new methods and the corresponding analysis is much more complicated than that in Blåsten, E., Liu, H. (2017). On vanishing near corners of transmission eigenfunctions. J. Funct. Anal. 273(11):3616–3632. Finally, as an interesting and practical application of the obtained geometric results, we establish a unique recovery result for the inverse problem associated with the transverse electromagnetic scattering by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductive parameter. [ABSTRACT FROM AUTHOR]

In this paper, a novel ultrawideband (UWB) time reversal technique for through-the-wall imaging (TWI) is introduced. The proposed algorithm is based on utilization of spatial and UWB frequency data acquired by antenna array. Scattering data are obtained by transmitting a short pulse from the central transmitter and recording the received signal at each array element. Individual multistatic scattering data matrix according to each antenna is formed by casting the fine and coarse frequency samples of the scattering information. The resulting matrix is calibrated based on transmitter signal and fed into the DORT (French acronym for decomposition of the time reversal operator) algorithm. The performance of the proposed method is investigated numerically by applying it to discrete scatterers embedded in homogeneous and continuously random medium. Numerical results are presented to show the effectiveness and high efficiency of the proposed algorithm for TWI. [ABSTRACT FROM AUTHOR]

In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with compact support. It is proved that an acoustically sound-soft or sound-hard surface can be uniquely determined by the far-field pattern of infinite number of incident plane waves with distinct directions. Moreover, a single point source or plane wave can be used to uniquely determine a scattering surface of polyhedral type. These uniqueness results apply to Maxwell equations with the perfectly conducting boundary condition. Our arguments rely on the mixed reciprocity relation in a half space and the reflection principle for Helmholtz and Maxwell equations. [ABSTRACT FROM AUTHOR]

The monotonicity method for the inverse acoustic scattering problem is to understand the inclusion relation between an unknown object and artificial one by comparing the far field operator with the artificial operator. This paper introduces the development of this method to the inverse crack scattering problem. Our aim is to give the following two indicators: One (Theorem 1.1) is to determine whether an artificial small arc is contained in the unknown arc. The other one (Theorem 1.2) is whether an artificial large domain contains the unknown one. Finally, numerical examples based on Theorem 1.1 are given. [ABSTRACT FROM AUTHOR]

We prove a conditional stability estimate of log-type for determining unknown boundaries from a single Cauchy data taken on an accessible sub-boundary. Our approach relies on new interior and boundary estimates for elliptic equations which are derived from the Carleman estimate. Stability results for target identification of an acoustic sound-soft scatterer from one or several far-field patterns are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside–outside duality method can be used to reconstruct the interior conductive eigenvalues. [ABSTRACT FROM AUTHOR]

In this work, the real-time non-destructive testing and evaluation (NDT/NDE) of faulty conductive tubes from eddy current (EC) measurements is addressed and solved in a computationally efficient way by means of an innovative learning-by-examples (LBE) methodology. More specifically, the estimation of the descriptors of a defect embedded within the cylindrical structure under test (SUT) is yielded by combining a non-linear feature extraction technique with an adaptive sampling strategy able to uniformly explore the arising feature space. Predictions are then performed during the on-line testing phase by means of a support vector regression (SVR). Representative results from a numerical/experimental validation are reported to assess the effectiveness of the proposed approach also in comparison with competitive state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inverse rough surface scattering problem in near-field optical imaging. This problem is actually to reconstruct the scattering surface as well as its impedance coefficient from multifrequency near-field data, and can be reduced into an integral scheme by employing an integral representation. We solve this integral scheme by a non-linear integral equation method, and further develop a fast inversion algorithm for reconstructing both the rough surface and the impedance coefficient. Numerical experiments are presented to illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the inverse scattering of an imperfectly conducting cylinder with corners is given by the Firefly Algorithm. The inverse problem is first transformed into a nonlinear optimization problem, and then solved by the Firefly Algorithm. To treat a target with corners, the target shape is modeled by the cubic spline interpolation. The Firefly Algorithm utilized in this study is a biologically inspired algorithm. It has been proved to be efficient with high success rate. Since the inverse scattering involves complicated computation, the Firefly Algorithm is a good candidate for reconstructing the target information. [ABSTRACT FROM AUTHOR]

In this note, the scattering operator of an asymptotically hyperbolic manifold is only allowed to act on functions supported on the source set where is an open subset of the boundary, and the resulting functions are then restricted to the observation set where Γ is open. When Γ is the complement of the closure of we call the corresponding operator the off-diagonal scattering operator with respect to We prove that for a non-empty open proper subset such that the intersection of its closure and its complement is not empty, the off-diagonal scattering operator with respect to determines the manifold modulo isometries which are equal to the identity at the boundary. We also prove there is no analog of the L2 boundary controllability from an open subset of the boundary for radiation fields, which presents a possible obstacle to extending the inverse result for arbitrary disjoint subsets and [ABSTRACT FROM AUTHOR]

The inverse acoustic scattering of point sources by a penetrable cavity and the external obstacle is considered. Making use of the internal measurements of scattered field on a closed curve inside the cavity, we first derive a factorization method which provides a rigorous characterization of the support of the cavity without knowing the external object. Then under the condition of the cavity is known in advance, we show that the linear sampling method can be applied to recover the outside obstacle with the help of some Green function. [ABSTRACT FROM AUTHOR]

The microwave imaging of buried targets from wide-band ground penetrating radar (GPR) signals is addressed. By considering a contrast source inversion (CSI) formulation of the inverse scattering equations and taking advantage of both the intrinsic frequency diversity of GPR data and the sparseness of the unknown buried scatterers within the subsurface domain of investigation, a multi-task Bayesian compressive sensing (MT-BCS) approach is integrated within a frequency hopping (FH) inversion scheme. Towards this end, an innovative “constrained” relevance vector machine (C-RVM) solver is developed to effectively exploit the information, progressively acquired at each frequency step, on the unknown scattering scenario. Representative numerical benchmarks and preliminary experimental results are presented to assess the effectiveness and the potentialities of the proposed subsurface imaging method (namely, the FH-MT-BCS technique). [ABSTRACT FROM AUTHOR]

This paper discusses an inverse scattering problem for the reconstruction of permittivity distribution of two-dimensional dielectric objects. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equation is derived and the imaging problem is reformulated into optimization problem. We solved the problem by combining subspace-based algorithm and self-adaptive dynamic differential evolution (SADDE). SADDE can process numerous unknowns of electromagnetic imaging problems. Different scatterers and environment have used to verify the stability of subspace-based algorithm and SADDE. We also compare genetic algorithm (GA) to show the robustness and the searching speed of SADDE. Numerical results show that the permittivity distribution of the dielectric objects is well reconstructed by SADDE. [ABSTRACT FROM PUBLISHER]

We study the inverse scattering problem with fixed observation angle data for a non-linear Schrödinger equation in 2D. We show that the main singularities of an unknown potential can be recovered from the Born approximation. Numerical examples are given to illustrate the method. [ABSTRACT FROM AUTHOR]

In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First, we appeal to the Born approximation for reconstructing small isotropic scatterers via the MUSIC algorithm. Some numerical reconstructions using the MUSIC algorithm are provided for reconstructing the scatterer and piecewise constant refractive index using a Bayesian method. We then consider the reconstruction of an anisotropic extended scatterer by a modified linear sampling method and the factorization method applied to the near field operator. This provides a rigorous characterization of the support of the anisotropic obstacle in terms of a range test derived from the measured data. Under appropriate assumptions on the material parameters, the derived factorization can be used to determine the support of the medium without a priori knowledge of the material properties. [ABSTRACT FROM PUBLISHER]

This paper is concerned with efficient numerical methods for solving the time-dependent scattering and inverse scattering problems of acoustic waves in a locally perturbed half-plane. By symmetric continuation, the scattering problem is reformulated as an equivalent symmetric problem defined in the whole plane. The retarded potential boundary integral equation method is modified to solve the forward problem. Then we consider the inverse scattering problem of determinating the local perturbation from the measured scattered data. The time domain linear sampling method is employed to deal with the inverse problem. The computation schemes proposed in this paper are relatively simple and easy to implement. Several numerical examples are presented to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

We introduce an imaging technique, the reciprocity gap (RG) method, for target detection for the borehole geo-radar. The RG method is based on the linear sampling method which has been studied extensively in the mathematical community recently. Based on the RG method, we propose a modified reciprocity gap (MRG) method. As the RG method, the MRG method makes no particular assumptions of buried targets. The technique is fast since it only involves the solution of ill-posed linear integral equations. Moreover, the MRG uses an approximate homogeneous background, Green's function, when the background medium is inhomogeneous (or unknown) in the measurement domain. Synthetic examples are given to show the performance of the RG method and the MRG method. [ABSTRACT FROM AUTHOR]

We propose a new integral equation formulation to characterize and compute transmission eigenvalues for constant refractive index that play an important role in inverse scattering problems for penetrable media. As opposed to the recently developed approach by Cossonnière and Haddar [1,2] which relies on a two by two system of boundary integral equations our analysis is based on only one integral equation in terms of Dirichlet-to-Neumann or Robin-to-Dirichlet operators which results in a noticeable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further we employ the numerical algorithm for analytic non-linear eigenvalue problems that was recently proposed by Beyn [3] for the numerical computation of transmission eigenvalues via this new integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the interior transmission eigenvalue problem for an inhomogeneous media with conductive boundary conditions. We prove the discreteness and existence of the transmission eigenvalues. We also investigate the inverse spectral problem of gaining information about the material properties from the transmission eigenvalues. In particular, we prove that the first transmission eigenvalue is a monotonic function of the refractive indexnand boundary conductivity parameter, and obtain a uniqueness result for constant coefficients. We provide some numerical examples to demonstrate the theoretical results in three dimensions. [ABSTRACT FROM AUTHOR]

We continue our investigation of transmission eigenvalues for spherically stratified media. In particular, in the case when the index of refractionn(r) is such that, we establish conditions onn(r) to guarantee that there exists an infinite number of complex transmission eigenvalues and when, we establish very weak conditions onn(r) to guarantee the existence of complex transmission eigenvalues. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse problem of reconstructing an infinite, locally rough interface from the scattered field measured on line segments above and below the interface in two dimensions. We extend the Kirsch-Kress method originally developed for inverse obstacle scattering problems to the above inverse transmission problem with unbounded interfaces. To this end, we reformulate our inverse problem as a nonlinear optimization problem with a Tikhonov regularization term. We prove the convergence of the optimization problem when the regularization parameter tends to zero. Finally, numerical experiments are carried out to show the validity of the inversion algorithm. [ABSTRACT FROM AUTHOR]

This research investigated imaging quality of two important methods widely used in electromagnetic inverse scattering problems. The algorithms, time reversal (TR) and linear sampling method (LSM), were compared for resolution of point imaging and a correlation indicator to determine image quality. Comparisons were made in single- and multifrequency modes for 2D scenarios in free-space. Comparisons revealed that resolution of TR is much better than LSM. In order to compare the total reconstructed images, several cases were considered to determine a comprehensive conclusion. The simulations were done based on experimental data. In this case, comparisons showed that in the term of correlation indicator, LSM surpasses TR. [ABSTRACT FROM PUBLISHER]

In this paper, we study the inverse scattering of tapered waves from sound soft surfaces or horizontally polarized electromagnetic waves from perfectly conducting surfaces. By the related Fréchet derivative with respect to a given surface of the solution of direct scattering problems, an efficient algorithm is proposed to reconstruct the parameters of unbounded rough surfaces from a set of scattered field measurements. Tapered wave is introduced to realize the asymptotic truncation for unbounded fractal rough surface. In order to improve the results of reconstruction, multi-angle and multi-frequency incidence strategy has been used. The numerical results show that the method yields satisfactory reconstructions for some rough surface profiles. [ABSTRACT FROM PUBLISHER]

In an effort to improve the performance of the linear sampling method in situations involving sparse data-sets, this method in inverse scattering has recently been extended from the frequency domain to the time domain. In this paper, we consider the relative merits of the time and multifrequency linear sampling methods for sparse, limited aperture, and data-sets. Among our conclusions are that, for limited aperture measurements single-frequency data can fail to reconstruct the scatterer, whereas both time and multifrequency domain data perform satisfactorily. On the other hand, if the aperture is too small all the sampling methods fail and increasing the number of measurements in a fixed size aperture is of no help. [ABSTRACT FROM AUTHOR]

This work studies the direct and inverse fixed energy scattering problem for the two-dimensional Schrödinger equation with a rather limited nonlinear index of refraction. In particular, using the Born approximation, we prove that all singularities of the unknown compactly supported potential belonging incan be obtained uniquely by the scattering data with fixed positive energy. The proof is based on the new estimates for the Faddeev Green’s function in. The main achievement here is the computation of the Born approximation, which is carried out using the total variation regularization method. Numerical examples with noisy data are given to illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

We present an inverse scattering method using only total electric field data on an observation surface with no knowledge of incident fields. An initial-boundary value problem is set up whose solution coincides with that of the original scattering problem in the interior region bounded by the observation surface if and only if a medium inside the observation surface is the same as that of the original one. A cost functional consisting the stored energy of the misfit field between the original problem and the boundary value problem with an estimated object is introduced to solve the inverse problem. Preliminary numerical examples are provided to assess the proposed inversion approach. [ABSTRACT FROM PUBLISHER]

A 2D complete identification algorithm for dielectric and multiple objects immersed in air is presented. The employed technique consists of initially retrieving the shape and position of the scattering object using a linear sampling method and then determining the electric permittivity and conductivity of the scatterer using adjoint sensitivity analysis. This inversion algorithm results in high computational speed and efficiency, and it can be generalized for any scatterer structure. Also, this method is robust with respect to noise. The numerical results clearly show that this hybrid approach provides accurate reconstructions of various objects. [ABSTRACT FROM PUBLISHER]

A microwave imaging technique based on particle swarm optimization (PSO) and asynchronous particle swarm optimization (APSO) are proposed for the electromagnetic inverse scattering. In this article, the finite-difference time-domain (FDTD) method is employed for the analysis of the forward scattering part, while PSO and/or APSO schemes (combining with FDTD) are applied to tackle the inverse scattering part. These two schemes aim for the simultaneous reconstruction of the location, shape, and permittivity of the dielectric scatterer in a slab medium. The reconstruction is based on the minimization of a cost functional, which evaluates the difference between measured and estimated values of the electric field. These two schemes are tested by several numerical examples, and the numerical results indicate that APSO outperforms PSO in terms of reconstruction accuracy and convergence speed. Both techniques have been tested in the case of simulated measurements contaminated by additive white Gaussian noise. [ABSTRACT FROM AUTHOR]

This paper introduces a general inversion method to simultaneously reconstruct scatterers with different boundary conditions such as Dirichlet, Neumann, Robin, and transmission boundaries without a priori information on their locations, shapes, or physical properties. The forward scattering of mixed scatterers is modeled by a unified framework of T-matrix method, while the objective function considered in the inverse problem is solved by a subspace-based optimization method. The unknowns are T-matrix coefficients, from which the types of boundary conditions of scatterers are identified. Numerical examples show that this method is able to recover not only the shapes of scatterers but also their physical properties and parameters. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the two-dimensional (2D) inverse acoustic scattering by a sound-soft, infinite rough surface. Our approach to this problem is based on the nonlinear integral equation method which was developed by Kress and Rundell for bounded obstacles. By using multiple frequency data, we derive a stable and accurate reconstruction method to image the profile of the rough surface. Numerical experiments are presented to illustrate the effectiveness of the inversion method. [ABSTRACT FROM PUBLISHER]

We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a variable index of refraction by the fixed incident-direction scattering amplitude. The inverse problem is formally posed with such measurement data. The second one is a global uniqueness in determining a constant refractive index by a single far-field measurement. The arguments are based on the study of certain non-self-adjoint interior transmission eigenvalue problems. [ABSTRACT FROM PUBLISHER]

This article presents an inverse scattering problem for recovering the shape and conductivity of an imperfect conductor buried in a half space by self-adaptive dynamic differential evolution (SADDE). The imperfect conductor of unknown conductivity and shapes is buried in one half-space and illuminated by the transverse magnetic plane wave from the other half-space. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equation is derived and the imaging problem is reformulated into optimisation problem. The SADDE algorithm is employed to find out the global extreme solution of the object function. Numerical results show that the conductivity and the shape of the conductor are well reconstructed. Moreover, the shape function is more sensitive to the scattered field variation than the conductivity. Accurate reconstruction of the shape function can be obtained by using the novel optimisation algorithm. As a result, the electric conductivity can be computed more accurately. [ABSTRACT FROM AUTHOR]

The inverse scattering problem in two-layered background that arises in near-field optics is discussed. The reconstruction of the scatterer from inhomogeneous medium deposited on a homogeneous substrate is presented, where the measured data only lies on a limited aperture. An error bound of the Born approximation is given. A moment method with truncated SVD is developed to handle the exponentially ill-posed problem with noisy measured data. Numerical experiments are presented to illustrate the resolution of the method, which are satisfying even under the perturbed data. [ABSTRACT FROM AUTHOR]

In this paper, an analytical reconstruction of the radiating current for the inverse scattering problem with a line measurement configuration is presented. Here, a generalized continuous singular value decomposition (SVD) of the scattering integral operator is extracted by means of the spectral representation of Green’s function. The proposed formulation can be used in analyzing image resolution and reconstruction of the radiating currents. In addition, the singular value spectrum relation with radiating/non-radiating modes is studied. Study of the singular spectrum gives the opportunity to investigate the growing behavior of evanescent modes and the sub-wavelength focusing property in double negative slab. The singular value spectrum plays an important role in the truncation process of analytical SVD. By virtue of the proposed analytical method, the equivalent current reconstruction can be done in a very short computation time. In addition, the singular system description is based on medium Green’s function and it is applicable to 2-D inverse scattering problems. [ABSTRACT FROM PUBLISHER]

Full polarimetric target recognition used in polarimetric synthetic aperture radar enables implementation of the recognition and classification of remote sensing images. This article investigates the classification of targets by target decomposition parameters, such as the scattering mechanism angle (α), anisotropy (A), and entropy (H), by using a new look-up table of region. The look-up table of region method is based on the combination of the H−A and A−α parameters. Because of the statistical properties of scatterers, the use of deterministic techniques, such as target decomposition, cannot be used. In these conditions, the look-up table of region is essentially required to evaluate the target parameters and classification of radar images. The goal of this study is the estimation of the polarimetric signatures, i.e., α/A/H, via a novel approach including the combination of target decomposition and look-up table of region. Data have been provided by the European Space Agency. Results show that the technique is excellent for target recognition and classification in statistical regions. [ABSTRACT FROM AUTHOR]

This paper concerns the shape identification problem of anisotropic periodic structures which are known as diffraction gratings. We study the so-called Factorization method as a tool for reconstructing the anisotropic periodic media from measured spectral data involving scattered electromagnetic waves in TM modes. This sampling method provides a simple criterion to compute a picture of shape of diffraction gratings in a rapid way. We propose a rigorous analysis for the method as well as numerical experiments to examine its performance. [ABSTRACT FROM AUTHOR]

We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method. [ABSTRACT FROM AUTHOR]

We consider inverse obstacle scattering problems for the wave equation with Robin or Neumann boundary conditions. The problem of reconstructing the geometry of such obstacles from measurements of scattered waves in the time domain is tackled using a time domain linear sampling method. This imaging technique yields a picture of the scatterer by solving a linear operator equation involving the measured data for many right-hand sides given by singular solutions to the wave equation. We analyse this algorithm for causal and smooth impulse shapes, we discuss the effect of different choices of the singular solutions used in the algorithm, and finally we propose a fast FFT-based implementation. [ABSTRACT FROM AUTHOR]