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This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

Analysis of PDEs · Mathematics 2025-07-02 Jianliang Li , Peijun Li , Xu Wang , Guanlin Yang

We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…

Analysis of PDEs · Mathematics 2024-10-31 Safiere Kuijpers , Laura Scarabosio

In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…

Analysis of PDEs · Mathematics 2021-04-21 Isaac Harris

When a macroscopic-sized non-crystalline sample is illuminated using coherent x-ray radiation, a bifurcation of photon energy flow may occur. The coarse-grained complex refractive index of the sample may be considered to attenuate and…

This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer…

Numerical Analysis · Mathematics 2024-12-20 Xiaoli Liu , Ruming Zhang

In this work, we construct the Born and inverse Born approximation and series to recover two function-valued coefficients in the Helmholtz equation for inverse scattering problems from the scattering data at two different frequencies. An…

Numerical Analysis · Mathematics 2025-03-18 Fioralba Cakoni , Shixu Meng , Zehui Zhou

This paper concerns the time-harmonic direct and inverse elastic scattering by an extended rigid elastic body surrounded by a finite number of point-like obstacles. We first justify the point-interaction model for the Lam\'{e} operator…

Mathematical Physics · Physics 2019-11-26 Guanghui Hu , Andrea Mantile , Mourad Sini , Tao Yin

This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…

Analysis of PDEs · Mathematics 2023-12-08 Heping Dong , Peijun Li

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…

Numerical Analysis · Mathematics 2026-04-28 Guanqiu Ma , Hongxia Guo , Guanghui Hu

We study an inverse scattering problem for Maxwell's equations in terminating waveguides, where localized reflectors are to be imaged using a remote array of sensors. The array probes the waveguide with waves and measures the scattered…

Numerical Analysis · Mathematics 2015-10-27 Liliana Borcea , Dinh-Liem Nguyen

Dealing with the inverse source problem for the scalar wave equation, we have shown recently that we can reconstruct the space-time dependent source function from the measurement of the wave, collected at a single point $x$ for a large…

Analysis of PDEs · Mathematics 2023-11-15 Soumen Senapati , Mourad Sini , Haibing Wang

This paper is concerned with inverse scattering problems of determining the support of an isotropic and homogeneous penetrable body from knowledge of multi-static far-field patterns in acoustics and in linear elasticity. The normal…

Analysis of PDEs · Mathematics 2024-04-11 Chun Liu , Guanghui Hu , Jianli Xiang , Jiayi Zhang

In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…

Analysis of PDEs · Mathematics 2023-05-16 Hongyu Liu , Shiqi Ma

We consider an inverse scattering problem to identify the locations or shapes of unknown anomalies from scattering parameter data collected by a small number of dipole antennas. Most of researches does not considered the influence of dipole…

Numerical Analysis · Mathematics 2018-09-18 Won-Kwang Park

This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…

Numerical Analysis · Mathematics 2025-09-25 Kai Li , Bo Zhang , Haiwen Zhang

The inverse scattering transform is extended to investigate the Tzitz\'{e}ica equation. A set of sectionally analytic eigenfunctions and auxiliary eigenfunctions are introduced. We note that in this procedure, the auxiliary eigenfunctions…

Exactly Solvable and Integrable Systems · Physics 2020-11-30 Linlin Wang , Junyi Zhu

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover…

Analysis of PDEs · Mathematics 2021-12-24 Yan Chang , Yukun Guo

Inverse scattering methods capable of compressive imaging are proposed and analyzed. The methods employ randomly and repeatedly (multiple-shot) the single-input-single-output (SISO) measurements in which the probe frequencies, the incident…

Data Analysis, Statistics and Probability · Physics 2015-05-14 Albert C. Fannjiang

This paper proposes a neural network approach for solving two classical problems in the two-dimensional inverse wave scattering: far field pattern problem and seismic imaging. The mathematical problem of inverse wave scattering is to…

Computational Physics · Physics 2019-12-02 Yuwei Fan , Lexing Ying