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This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…

Analysis of PDEs · Mathematics 2026-01-19 Chengyu Wu , Jiaqing Yang

In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…

Analysis of PDEs · Mathematics 2020-09-10 Florian Faucher , Otmar Scherzer , Hélène Barucq

Many inverse problems arising in engineering and applied sciences involve unknown quantities with pronounced spatial inhomogeneity, such as localized defects or spatially varying material properties, making reliable uncertainty…

Numerical Analysis · Mathematics 2026-02-10 Babak Maboudi Afkham , Tomas Soto , Mirza Karamehmedovic , Lassi Roininen

This paper addresses the inverse scattering problem for Maxwell's equations. We first show that a bianisotropic scatterer can be uniquely determined from multi-static far-field data through the factorization analysis of the far-field…

Numerical Analysis · Mathematics 2025-02-03 Thu Le , Dinh-Liem Nguyen

An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…

Mathematical Physics · Physics 2007-05-23 A. S. Blagovestchenskii , Y. Kurylev , V. Zalipaev

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

Statistics Theory · Mathematics 2015-06-15 Sebastian J. Vollmer

A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…

Numerical Analysis · Mathematics 2023-06-13 Deyue Zhang , Yan Chang , Yukun Guo

In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…

Numerical Analysis · Mathematics 2026-01-23 Shutong Hou , Mourad Sini , Haibing Wang

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

We deal with the inverse problem of reconstructing acoustic material properties or/and external sources for the time-domain acoustic wave model. The traditional measurements consist of repeated active (or passive) interrogations, as the…

Analysis of PDEs · Mathematics 2025-07-15 Soumen Senapati , Mourad Sini

We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order term. The medium is characterized by a spatially varying…

Analysis of PDEs · Mathematics 2026-03-26 Giovanni Covi , Maarten de Hoop , Mikko Salo

The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…

Numerical Analysis · Mathematics 2016-12-14 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen , Hui Liu

We use a new method to prove uniqueness theorem for a coefficient inverse scattering problem without the phase information for the 3-D Helmholtz equation. We consider the case when only the modulus of the scattered wave field is measured…

Mathematical Physics · Physics 2017-09-13 Michael V. Klibanov , Vladimir G. Romanov

Scattering properties of a material are changed when the material is injected with small acoustically soft particles. It is shown that its new scattering behavior can be understood as a solution of a potential scattering problem with the…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm , S. Gutman

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…

Analysis of PDEs · Mathematics 2015-05-18 Xiaodong Liu , Bo Zhang , Jiaqing Yang

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method…

Numerical Analysis · Mathematics 2015-06-12 Kazufumi Ito , Bangti Jin , Jun Zou

We consider the problem of determining the shape and location of an unknown penetrable object in a perfectly conducting electromagnetic waveguide. The inverse problem is posed in the frequency domain and uses multistatic data in the near…

Numerical Analysis · Mathematics 2019-09-04 Peter Monk , Virginia Selgas , Fan Yang

This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging…

Numerical Analysis · Mathematics 2024-10-10 Deyue Zhang , Mengjiao Bai , Yan Chang , Yukun Guo

A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…

Mathematical Physics · Physics 2014-12-30 Sergey Leble , Irina Vereshchagina