Related papers: A note on the enclosure method for an inverse obst…
In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…
This work is concerned with an inverse electromagnetic scattering problem in two dimensions. We prove that in the TE polarization case, the knowledge of the electric far-field pattern incited by a single incoming wave is sufficient to…
The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…
We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the…
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…
This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…
We consider an inverse shape problem for recovering an unknown simply supported obstacle in two dimensions from near--field point--source measurements for the biharmonic Helmholtz equation. The measured data consist of the scattered field…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
It is proved that the scattering amplitude $A(\beta, \alpha_0, k_0)$, known for all $\beta\in S^2$, where $S^2$ is the unit sphere in $\mathbb{R}^3$, and fixed $\alpha_0\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the…
In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and…
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
We propose a novel on-surface radiation condition to approximate the outgoing solution to the Helmholtz equation in the exterior of several impenetrable convex obstacles. Based on a local approximation of the Dirichlet-to-Neumann operator…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…
In this paper we consider the classic problems of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries. The scattering problems are formulated as integral equations and solved using a Nystr\"om scheme…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…