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We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…

Analysis of PDEs · Mathematics 2024-12-20 Alexander Konschin , Armin Lechleiter

This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source in linear elasticity. The approach also applies to the compressional (resp. shear) part of the…

Numerical Analysis · Mathematics 2025-08-25 Guanqiu Ma , Guanghui Hu

We consider the inverse scattering problem for inhomogeneous media of compact support governed by the fractional s-Helmholtz equation, with $0<s<1$, in dimensions $d=1,2,3$. In particular, we study the determination of the support of the…

Analysis of PDEs · Mathematics 2026-04-30 Dana Zilberberg

In this paper, we develop a factorization method to reconstruct cavities in a heat conductor by knowing the Neumann-to-Dirichlet map at the boundary of this conductor. The factorization method is a very well known reconstruction method for…

Mathematical Physics · Physics 2019-12-30 Jun Guo , Gen Nakamura , Haibing Wang

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…

Numerical Analysis · Mathematics 2018-07-26 Armin Lechleiter , Ruming Zhang

This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the…

Numerical Analysis · Mathematics 2021-07-02 Xiaodong Liu , Shixu Meng , Bo Zhang

Experimental aeroacoustics is concerned with the estimation of acoustic source power distributions, which are for instance caused by fluid structure interactions on scaled aircraft models inside a wind tunnel, from microphone array…

Numerical Analysis · Mathematics 2022-10-05 Roland Griesmaier , Hans-Georg Raumer

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

We consider the scattering of time-harmonic plane waves by a compactly supported inhomogeneous scattering obstacle governed by the Helmholtz equation. Given far field observations of the scattered fields corresponding to plane wave incident…

Numerical Analysis · Mathematics 2026-02-03 Roland Griesmaier , Bastian Harrach , Jianli Xiang

An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…

Numerical Analysis · Mathematics 2014-04-30 Ying Li

The factorization method by Kirsch (1998) provides a necessary and sufficient condition for characterizing the shape and position of an unknown scatterer by using far-field patterns of infinitely many time-harmonic plane waves at a fixed…

Numerical Analysis · Mathematics 2025-08-25 Guanqiu Ma , Guanghui Hu

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

Numerical Analysis · Mathematics 2015-05-28 Carlos Borges , Leslie Greengard

In this paper, we consider the inverse problem of recovering a doubly periodic Lipschitz structure through the measurement of the scattered field above the structure produced by point sources lying above the structure. The medium above the…

Analysis of PDEs · Mathematics 2015-05-18 Guanghui Hu , Bo Zhang

In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic…

Analysis of PDEs · Mathematics 2017-01-18 Isaac Harris , Scott Rome

Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the Lipschitz boundary of a bounded obstacle…

Analysis of PDEs · Mathematics 2020-06-15 Andrea Mantile , Andrea Posilicano

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…

Mathematical Physics · Physics 2024-02-13 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

The 3-d inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. The main difference with the conventional inverse scattering problems is that only the…

Mathematical Physics · Physics 2016-01-20 Michael V. Klibanov , Vladimir G. Romanov

We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…

Analysis of PDEs · Mathematics 2023-03-22 Lei Zhang , Yue Zhao

We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…

Spectral Theory · Mathematics 2008-11-20 Anne Boutet de Monvel , Iryna Egorova , Gerald Teschl

We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…

Analysis of PDEs · Mathematics 2022-02-14 Roland Griesmaier , Marvin Knöller , Rainer Mandel