In this paper we establish a factorization method for recovering the location and shape of an acoustic bounded obstacle with using the near-field data, corresponding to infinitely many incident point sources. The obstacle is allowed to be an impenetrable scatterer of sound-soft, sound-hard or impedance type or a penetrable scatterer. An outgoing-to-incoming operator is constructed for facilitating the factorization of the near-field operator, which can be easily implemented numerically. Numerical examples are presented to demonstrate the feasibility and effectiveness of our inversion algorithm, including the case where limited aperture near-field data are available only.

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This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle with buried objects inside. We prove under certain conditions that the factorization method can be applied to reconstruct the penetrable obstacle from far-field data without knowing the buried objects inside. Numerical examples are also provided illustrating the inversion algorithm. Introduction.In this paper, we study the problem of scattering of timeharmonic acoustic plane waves by an inhomogeneous penetrable obstacle with buried objects inside. This type of problem occurs in various applications such as radar, remote sensing, geophysics, medical imaging, and nondestructive testing. Let D 0 denote an impenetrable obstacle which is embedded in a bounded, penetrable obstacle D with C 2 -boundary ∂D, that is, D 0 ⊂ D. Assume that D 1 := D \ D 0 is filled with an inhomogeneous material characterized by the refractive index n ∈ L ∞ (D 1 ) with Re[n(x)] > 0 and Im[n(x)] ≥ 0 for almost all x ∈ D 1 and D 2 := R 3 \ D is filled with a homogeneous material with the constant refractive index 1. Then the scattering of time-harmonic acoustic waves by D and D 0 can be modeled by the Helmholtz equation with boundary conditions on the interface ∂D and boundary ∂D 0 :

This paper is concerned with the inverse scattering problem of reconstructing the support of a periodic inhomogeneous medium from knowledge of the scattered field measured on a straight line above and below the periodic structure. A linear sampling method is proposed to reconstruct the support of the periodic inhomogeneous medium based on a linear operator equation. The mathematical analysis of the sampling method is developed and numerical examples are given showing the practicality of the reconstruction algorithm.

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the inhomogeneous penetrable obstacle can be uniquely determined from the far-field pattern at a fixed frequency, disregarding its contents. Our method is based on constructing a well-posed interior transmission problem in a small domain associated with the Helmholtz or modified Helmholtz equation and the Maxwell or modified Maxwell equations. A key role is played by the smallness of the domain which ensures that the lowest transmission eigenvalue is large so that a given wave number k is not an eigenvalue of the interior transmission problem. Another ingredient in our proofs is a priori estimates of solutions to the transmission scattering problems with data in L p (1 < p < 2), which are established in this paper by using the integral equation method. A main feature of the new method is that it can deal with the acoustic and electromagnetic cases in a unified way and can be easily applied to deal with inverse scattering by unbounded rough interfaces.

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