Related papers: On the numerical solution to an inverse medium pro…
This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce…
This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz-Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive…
In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…
We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of…
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…
We deal with the stability issue for the determination of outgoing time-harmonic acoustic waves from their far-field patterns. We are especially interested in keeping as explicit as possible the dependence of our stability estimates on the…
We study the inverse problem of qualitatively recovering a supported cavity in a thin elastic plate governed by the flexural (biharmonic) wave equation, using far-field pattern measurements. We derive a reciprocity principle and a…
This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…
The fixed energy scattering matrix is defined on a perturbed stratified medium, and for a class of perturbations, its main part is shown to be a Fourier integral operator on the sphere at infinity. This is facilitated by developing a…
This paper is concerned with the unique identification of the shape of a scatterer through a single far-field pattern in an inverse elastic medium scattering problem with a generalized transmission boundary condition. The uniqueness issue…
We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…
This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
Inverse scattering in layered media has a wide range of applications, examples including geophysical exploration, medical imaging, and remote sensing. In this paper, we develop a selective focusing method for identifying multiple unknown…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
We propose a novel indicator function for reconstructing acoustic sources from multi-frequency near-field measurements. The theoretical basis is established by a formula relating the scattered field to the source function through the Radon…
This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…
In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti's formula (direct…
For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…