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We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…

Computer Vision and Pattern Recognition · Computer Science 2016-10-07 Hsiou-Yuan Liu , Ulugbek S. Kamilov , Dehong Liu , Hassan Mansour , Petros T. Boufounos

Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…

Analysis of PDEs · Mathematics 2025-11-06 Thorsten Hohage , Meng Liu

We consider the electromagnetic scattering from a convex polyhedral PEC or PMC obstacle due to a time-harmonic incident plane wave. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain…

Analysis of PDEs · Mathematics 2017-03-08 Jingzhi Li , Hongyu Liu , Yuliang Wang

We study the numerical approximation of the inverse scattering problem in the two-dimensional homogeneous isotropic linear elasticity with an unknown linear load given by a square matrix. For both backscattering data and fixed-angle…

Analysis of PDEs · Mathematics 2022-05-20 J. A. Barceló , C. Castro , M. C. Vilela

This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source…

Numerical Analysis · Mathematics 2022-12-12 Hongxia Guo , Guanghui Hu , Mengjie Zhao

This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…

Computational Engineering, Finance, and Science · Computer Science 2018-11-29 Yuval Harness

In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary. We will assume that the corresponding far-field pattern is known/measured and we consider two inverse problems.…

Analysis of PDEs · Mathematics 2024-04-04 Victor Hughes , Isaac Harris , Heejin Lee

This paper concerns the reconstruction of the scattering coefficient in a two-dimensional transport equation from angularly averaged measurements when the probing source is isotropic and time-harmonic. This is a practical setting in the…

Analysis of PDEs · Mathematics 2011-10-17 Guillaume Bal , Francois Monard

The paper is devoted to investigating a Cauchy problem for nonlinear elliptic PDEs in the abstract Hilbert space. The problem is hardly solved by computation since it is severely ill-posed in the sense of Hadamard. We shall use a modified…

Analysis of PDEs · Mathematics 2015-12-10 Nguyen Huy Tuan , Le Duc Thang , Vo Anh Khoa

This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can…

Numerical Analysis · Mathematics 2022-12-20 Deyue Zhang , Yue Wu , Yukun Guo

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

In this article, we propose a non-parametric Bayesian level-set method for simultaneous reconstruction of two different piecewise constant coefficients in an elliptic partial differential equation. We show that the Bayesian formulation of…

Applications · Statistics 2025-05-28 Anuj Abhishek , Thilo Strauss , Taufiquar Khan

We propose a direct imaging method based on the reverse time migration to reconstruct extended obstacles in the half space with finite aperture elastic scattering data at a fixed frequency. We prove the resolution of the reconstruction…

Numerical Analysis · Mathematics 2019-07-24 Zhiming Chen , Shiqi Zhou

This paper investigates the inverse scattering problem for the magnetic Schr\"odinger equation. We first establish the well-posedness of the direct problem through a variational approach under physically meaningful assumptions on the…

Analysis of PDEs · Mathematics 2025-10-10 Chaohua Duan , Zhen Xue

The reconstruction of physical properties of a medium from boundary measurements, known as inverse scattering problems, presents significant challenges. The present study aims to validate a newly developed convexification method for a 3D…

Numerical Analysis · Mathematics 2023-06-02 Thuy Le , Vo Anh Khoa , Michael Victor Klibanov , Loc Hoang Nguyen , Grant Bidney , Vasily Astratov

In this work the Lippmann-Schwinger equation is used to model seismic waves in strongly scattering acoustic media. We consider the Helmholtz equation, which is the scalar wave equation in the frequency domain with constant density and…

Computational Physics · Physics 2021-02-24 Kjersti Solberg Eikrem , Geir Nævdal , Morten Jakobsen

In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…

Numerical Analysis · Mathematics 2025-08-22 Tianhao Hu , Xinchi Huang , Bangti Jin , Qimeng Quan , Zhi Zhou

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki , Tao Yin

This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…

Analysis of PDEs · Mathematics 2019-12-02 Xueshuang Xiang , Hongpeng Sun

The aim of this paper is to extend the method of improving cloaking structures in the conductivity to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new…

Analysis of PDEs · Mathematics 2015-05-30 Habib Ammari , Hyeonbae Kang , Hyundae Lee , Mikyoung Lim