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Abstract This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform L α p ( 1 < p ≤ 2 ) $L^{p}_{\alpha }\ (1< p\leq 2)$ estimates for the scattered and transmitted wave fields corresponding to a series of incident point sources. Based on these a priori estimates and a mixed reciprocity relation, we prove that the penetrable structure can be uniquely identified by means of the scattered field measured only above the structure induced by a countably infinite number of quasi-periodic incident plane waves.

Abstract This paper is concerned with the inverse scattering of time-harmonic acoustic plane waves by a multi-layered fluid–solid medium in the three dimensional space. We establish the global uniqueness in identifying the embedded penetrable solid obstacle, the surrounding fluid medium and its wave number from the acoustic far-field pattern for all incident plane waves at a fixed frequency. The proof depends on constructing different kinds of interior transmission problems in appropriate small domains and the a priori estimates derived for both the elastic wave fields in the embedded solid obstacle and the acoustic wave fields in the surrounding fluid medium.

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves by a penetrable, inhomogeneous, Lipschitz obstacle covered with a thin layer of high conductivity. The well posedness of the direct problem is established by the variational method. The inverse problem is also considered in this paper. Under certain assumptions, a uniqueness result is obtained for determining the shape and location of the obstacle and the corresponding surface parameter λ(x) from the knowledge of the near field data, assuming that the incident fields are electric dipoles located on a large sphere with polarization p∈ℝ3. Our results extend those in the paper by F. Hettlich (1996) to the case of inhomogeneous Lipschitz obstacles.

This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on which a Neumann boundary condition is imposed. A novel integral equation formulation is proposed for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners and some closed smooth artificial curve. It is a nontrivial extension of our previous work on direct and inverse scattering by a locally rough surface from the Dirichlet boundary condition to the Neumann boundary condition [SIAM J. Appl. Math., 73 (2013), pp. 1811{1829]. For the Dirichlet boundary condition, the integral equation obtained is uniquely solvable in the space of bounded continuous functions on the bounded curve, and it can be solved eficiently by using the Nystrom method with a graded mesh. However, the Neumann condition case leads to an integral equation which is solvable in the space of squarely integrable functions on the bounded curve rather than in the space of bounded continuous functions, making the integral equation very dificult to solve numerically with the classic and eficient Nystrom method. In this paper, we make use of the recursively compressed inverse preconditioning method developed by Helsing to solve the integral equation which is eficient and capable of dealing with large wave numbers. For the inverse problem, it is proved that the locally rough surface is uniquely determined from a knowledge of the far-field pattern corresponding to incident plane waves. Moreover, based on the novel integral equation formulation, a Newton iteration method is developed to reconstruct the locally rough surface from a knowledge of multiple frequency far-field data. Numerical examples are also provided to illustrate that the reconstruction algorithm is stable and accurate even for the case of multiple-scale profiles. [ABSTRACT FROM AUTHOR]

In this paper we study the inverse scattering problem of identifying a two-layered cavity by internal acoustic measurements. A uniqueness result is first provided for the determination of the interior interface by measurements corresponding to many incident point sources. Then the factorization method is proved to be valid in reconstructing the interior interface by using the same measurements. Finally, we carry out several numerical examples to illustrate the practicability of the inversion algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse electromagnetic scattering by a two-layered medium in the non-magnetic case. We prove that both the electric permittivity and the conductivity can be uniquely recovered in an unknown annular domain by the internal wave-field measurements at one fixed frequency, if and are both assumed to be constant. Furthermore, we prove that the unknown annular domain can be also uniquely recovered using the same measurements. The method proposed in this paper essentially depends on the uniform a priori estimate for the scattered magnetic field in the sense when the incident fields are induced by a sequence of deformed electric dipoles. Another important ingredient for our method is to reconstruct well-defined PDE systems in a sufficiently small domain by using the solutions to the electromagnetic scattering problem in the two-layered cavity. [ABSTRACT FROM AUTHOR]

Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex inhomogeneous medium from the far-field data. Numerical examples are also provided to illustrate the practicability of the inversion algorithm. [ABSTRACT FROM AUTHOR]

Consider the inverse scattering problem of time-harmonic acoustic waves by a 3D bounded elastic obstacle which may contain embedded impenetrable obstacles inside. We propose a novel and simple technique to show that the elastic obstacle can be uniquely recovered by the acoustic far-field pattern at a fixed frequency, disregarding its contents. Our method is based on constructing a well-posed modified interior transmission problem on a small domain and makes use of an a priori estimate for both the acoustic and elastic wave fields in the usual H1-norm. In the case when there is no obstacle embedded inside the elastic body, our method gives a much simpler proof for the uniqueness result obtained previously in the literature (Natroshvili et al 2000 Rend. Mat. Serie VII 20 57–92; Monk and Selgas 2009 Inverse Problems Imaging3 173–98). [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with different kinds of unknown buried objects inside. By constructing a sequence of operators which are small perturbations of the far-field operator in a suitable way, we prove that each operator in this sequence has a factorization satisfying the Range Identity. We then develop an approximate factorization method for recovering the support of the inhomogeneous medium from the far-field data. Finally, numerical examples are provided to illustrate the practicability of the inversion algorithm. [ABSTRACT FROM AUTHOR]