English
Related papers

Related papers: Uniqueness and modified Newton method for cracks f…

200 papers

We study an inverse acoustic scattering problem by the Factorization Method when the unknown scatterer consists of two objects with different physical properties. Especially, we consider the following two cases: One is the case when each…

Analysis of PDEs · Mathematics 2021-06-16 Takashsi Furuya

The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…

Numerical Analysis · Mathematics 2021-05-26 Long Li , Jiansheng Yang , Bo Zhang , Haiwen Zhang

We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…

Analysis of PDEs · Mathematics 2013-10-15 Guanghui Hu , Jingzhi Li , Hongyu Liu , Hongpeng Sun

Modified Rayleigh conjecture (MRC) in scattering theory is proposed and justified. MRC allows one to develop numerical algorithms for solving direct scattering problems related to acoustic wave scattering by soft and hard obstacles of…

Mathematical Physics · Physics 2009-11-10 A. G. Ramm

We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…

Numerical Analysis · Mathematics 2021-04-29 Carlos Borges , Manas Rachh

This paper is concerned with the uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data generated by superpositions of two incident plane waves at a fixed frequency. It can be proved that the unknown…

Analysis of PDEs · Mathematics 2023-07-25 Xiaoxu Xu

We transform an inverse scattering problem to be an interior transmission problem. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of…

Mathematical Physics · Physics 2015-08-06 Lung-Hui Chen

Inverse scattering focuses on recovering unknown scatterers from wave measurements. A fundamental challenge is determining whether an inverse obstacle problem can be resolved from a single far-field measurement, a task particularly…

Analysis of PDEs · Mathematics 2026-04-15 Huaian Diao , Hongyu Liu , Longyue Tao

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 is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or near-field data. A recursive Newton iteration…

Numerical Analysis · Mathematics 2017-06-06 Bo Zhang , Haiwen Zhang

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…

Numerical Analysis · Mathematics 2023-02-15 Carlos Borges , Manas Rachh , Leslie Greengard

In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft obstacle from the modulus of the far-field data for a single incident plane wave. By adding a reference ball artificially to the…

Numerical Analysis · Mathematics 2018-04-17 Heping Dong , Deyue Zhang , Yukun Guo

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…

Analysis of PDEs · Mathematics 2020-10-28 Tilo Arens , Xia Ji , Xiaodong Liu

We study the factorization and monotonicity method for inverse acoustic scattering problems. Firstly, we give a new general functional analysis theorem for the monotonicity method. Comparing with the factorization method, the general…

Analysis of PDEs · Mathematics 2021-06-16 Takashi Furuya

Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…

Analysis of PDEs · Mathematics 2016-07-20 Roland Griesmaier , John Sylvester

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…

Analysis of PDEs · Mathematics 2026-04-14 Jialei Li , Xiaodong Liu

Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…

Analysis of PDEs · Mathematics 2018-08-08 Xia Ji , Xiaodong Liu , Bo Zhang

In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile.…

Numerical Analysis · Mathematics 2019-01-29 Carlos Borges , George Biros

A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…

Analysis of PDEs · Mathematics 2018-08-01 Juan Liu , Jiguang Sun

This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident…

Analysis of PDEs · Mathematics 2020-02-19 Deyue Zhang , Yinglin Wang , Yukun Guo , Jingzhi Li