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In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…

Numerical Analysis · Mathematics 2020-10-28 Carlos Borges , Jun Lai

Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Direct Sampling Method). We present a modular framework that…

Numerical Analysis · Mathematics 2025-10-31 Guanyu Pan , Jianing Zhou , Xiaotong Liu , Yunqing Huang , Nianyu Yi

Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…

Analysis of PDEs · Mathematics 2018-12-27 Jianliang Li , Peijun Li

This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…

Numerical Analysis · Mathematics 2026-03-11 Fenglin Sun , Hongxia Guo

We consider the direct and inverse scattering problem for a penetrable, isotropic obstacle with a second-order Robin boundary condition, which asymptotically models the delamination of the boundary of the scatterer. We develop a direct…

Analysis of PDEs · Mathematics 2026-01-22 Govanni Granados , Isaac Harris , Andreas Kleefeld

An inverse scattering problems for the 3-D generalized Helmholtz equation is considered. Only the modulus of the complex valued scattered wave field is assumed to be measured and the phase is not measured. Uniqueness theorem is proved.

Mathematical Physics · Physics 2016-07-15 Michael V. Klibanov

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…

Analysis of PDEs · Mathematics 2018-01-18 Deyue Zhang , Yukun Guo , Jingzhi Li , Hongyu Liu

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

Source localization is the inverse problem of graph information dissemination and has broad practical applications. However, the inherent intricacy and uncertainty in information dissemination pose significant challenges, and the ill-posed…

Machine Learning · Computer Science 2023-04-19 Bosong Huang , Weihao Yu , Ruzhong Xie , Jing Xiao , Jin Huang

In the present work, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable…

Analysis of PDEs · Mathematics 2016-04-01 Erkinjon Karimov , Nasser Al-Salti , Sebti Kerbal

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…

Analysis of PDEs · Mathematics 2015-05-28 Mark Hubenthal

In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…

Analysis of PDEs · Mathematics 2019-11-27 Peijun Li , Xu Wang

This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…

Analysis of PDEs · Mathematics 2026-05-05 Erkinjon Karimov , Muzaffar Toshpulatov

We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a…

Analysis of PDEs · Mathematics 2013-08-28 Guanghui Hu , Hongyu Liu

In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…

Analysis of PDEs · Mathematics 2020-12-02 Zhiyuan Li , Zhidong Zhang

The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…

Optics · Physics 2009-09-15 Albert C. Fannjiang

Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a…

Numerical Analysis · Mathematics 2022-04-01 William W. Symes

We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the…

Analysis of PDEs · Mathematics 2015-02-05 Jingzhi Li , Hongyu Liu

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…

Methodology · Statistics 2026-03-10 Roxana Darvishi , David C. Stenning , Ted von Hippel , Owen G. Ward

A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…

Numerical Analysis · Mathematics 2020-04-10 Zhaoxing Li , Yanfang Liu , Jiguang Sun , Liwei Xu