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We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the…

Numerical Analysis · Mathematics 2023-03-21 Josselin Garnier , Houssem Haddar , Hadrien Montanelli

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…

Numerical Analysis · Mathematics 2025-06-03 Xiaoli Liu , Shixu Meng , Jialu Tian , Bo Zhang

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

In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here we will propose and…

Analysis of PDEs · Mathematics 2021-10-22 Isaac Harris

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

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

This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…

Analysis of PDEs · Mathematics 2020-08-05 Jianliang Li , Jiaqing Yang , Bo Zhang

With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…

Numerical Analysis · Mathematics 2021-05-04 Jiantang Zhang , Jin Cheng , Min Zhong

This paper is concerned with the inverse acoustic scattering problems of reconstructing time-dependent multiple point sources and sources on a curve $L$ of the form $\lambda(t)\tau(x)\delta_L(x)$. A direct sampling method with a novel…

Numerical Analysis · Mathematics 2023-09-07 Jiaru Wang , Bo Chen , Qingqing Yu , Yao Sun

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…

Numerical Analysis · Mathematics 2020-02-25 Trung Truong , Dinh-Liem Nguyen , Michael Klibanov

A method for the identification of small inhomogeneities from a surface data is presented in the framework of an inverse scattering problem for the Helmholtz equation. Using the assumptions of smallness of the scatterers one reduces this…

Mathematical Physics · Physics 2007-05-23 Semion Gutman , Alexander G. Ramm

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…

Analysis of PDEs · Mathematics 2016-07-25 Peijun Li , Ganghua Yuan

Regularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of…

Functional Analysis · Mathematics 2016-05-05 Gitta Kutyniok , Volker Mehrmann , Philipp Petersen

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…

Analysis of PDEs · Mathematics 2012-10-22 G. Giorgi , M. Brignone , R. Aramini , M. Piana

This paper presents an adaptive numerical framework for solving exterior "sound-soft" scattering problems governed by the Helmholtz equation. By interpreting the Method of Fundamental Solutions through the lens of rational approximation, we…

Numerical Analysis · Mathematics 2026-01-28 Stefano Costa

The paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end…

Analysis of PDEs · Mathematics 2019-11-05 Mozhgan Nora Entekhabi , Ajith Gunaratne

This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…

Numerical Analysis · Mathematics 2017-10-16 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen

The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…

Data Analysis, Statistics and Probability · Physics 2009-05-19 Albert Fannjiang , Pengchong Yan , Thomas Strohmer

The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a linear integral equation called…

Numerical Analysis · Mathematics 2022-03-16 Timo Lähivaara , Peter Monk , Virginia Selgas

We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…

Numerical Analysis · Mathematics 2022-07-21 Thu Le , Dinh-Liem Nguyen , Vu Nguyen , Trung Truong
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