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The long standing problem on finding the height correlation function is studied by the inverse scattering problem. We propose a new method in the frame work of Kirchhoff theory which we call "path derivation of scattered wave (PDSW)" in…
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit…
We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…
This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…
In this paper we consider the inverse acoustic scattering (in \mathbb{R}^3) or electromagnetic scattering (in \mathbb{R}^2, for the scalar TE-polarization case) problem of reconstructing possibly multiple defective penetrable regions in a…
In this paper, we consider an inverse electromagnetic medium scattering problem of reconstructing unknown objects from time-dependent boundary measurements. A novel time-domain direct sampling method is developed for determining the…
We construct a scattering matrix with operator valued entries describing solutions to the 1+1 wave equation where permittivities has memory and depends on time and space. It is the analogue of the scattering matrix for spatially localised…
This paper is concerned with the electromagnetic inverse scattering problem that aims to determine the location and shape of anisotropic scatterers from far field data (at a fixed frequency). We study the orthogonality sampling method which…
This article focuses on the analysis of three direct sampling indicators which can be used for recovering scatterers from the far-field pattern of time-harmonic acoustic measurements. These methods fall under the category of sampling…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
This paper is concerned with the inverse scattering problem for the three-dimensional Maxwell's equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic…
Scatterers in a homogeneous medium are imaged by probing the medium with two point sources of waves modulated by correlated signals and by measuring only intensities at one single receiver. For appropriately chosen source pairs, we show…
Optoacoustic image formation is conventionally based upon ultrasound time-of-flight readings from multiple detection positions. Herein, we exploit acoustic scattering to physically encode the position of optical absorbers in the acquired…
Bloch wavefunctions are used to derive dispersion relations for water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one dimensional periodicity (stripes), band gaps for wavevectors in…
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…
This paper concerns the time-harmonic direct and inverse elastic scattering by an extended rigid elastic body surrounded by a finite number of point-like obstacles. We first justify the point-interaction model for the Lam\'{e} operator…
We discuss the numerically stable, spectral-domain computation and extraction of the scattered electromagnetic field excited by distributed sources embedded in planar-layered environments, where each layer may exhibit arbitrary and…
We investigate the inverse scattering problem for tracking the location and orientation of a moving scatterer using a single incident field. We solve the problem by adopting the optimization approach with the objective function defined by…
In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…
Wave propagation through waveguides, quantum wires or films with a modest amount of disorder is in the semi-ballistic regime when in the transversal direction(s) almost no scattering occurs, while in the long direction(s) there is so much…