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In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we…

Analysis of PDEs · Mathematics 2023-05-25 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

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

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 consider the inverse scattering problem for time-harmonic acoustic waves in a medium with pointwise inhomogeneities. In the Foldy-Lax model, the estimation of the scatterers' locations and intensities from far field measurements can be…

Numerical Analysis · Mathematics 2024-07-25 Giovanni S. Alberti , Romain Petit , Matteo Santacesaria

In this paper we consider a dynamic computer simulator that produces a time-series response $y_t(x)$ over $L$ time points, for every given input parameter $x$. We propose a method for solving inverse problems, which refer to the finding of…

Methodology · Statistics 2020-12-15 Joseph Resch , Abhyuday Mandal , Pritam Ranjan

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

This paper investigates the inverse source problem with a single propagating mode at multiple frequencies in an acoustic waveguide. The goal is to provide both theoretical justifications and efficient algorithms for imaging extended sources…

Numerical Analysis · Mathematics 2023-02-24 Shixu Meng

This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…

Numerical Analysis · Mathematics 2020-08-13 Gang Bao , Yiwen Lin , Xiang Xu

This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and…

Numerical Analysis · Mathematics 2021-07-28 Zhipeng Yang , Xinping Gui , Ju Ming , Guanghui Hu

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer…

Numerical Analysis · Mathematics 2015-06-05 Kazufumi Ito , Bangti Jin , Jun Zou

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…

Computational Physics · Physics 2025-12-12 Olivia Tsang , Owen Melia , Vasileios Charisopoulos , Jeremy Hoskins , Yuehaw Khoo , Rebecca Willett

This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…

Analysis of PDEs · Mathematics 2018-08-01 Deyue Zhang , Yukun Guo , Jingzhi Li , Hongyu Liu

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

Methodology · Statistics 2023-02-09 Xiao Liu , Kyongmin Yeo

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…

Mathematical Physics · Physics 2011-11-10 Ole Henrik Waagaard , Johannes Skaar

In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the…

Analysis of PDEs · Mathematics 2021-07-20 Isaac Harris , Dinh-Liem Nguyen , Thi-Phong Nguyen

The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…

Analysis of PDEs · Mathematics 2021-12-03 Mourad Sini , Haibing Wang

Source enumeration, the task of estimating the number of sources from the signal received by the array of antennas, is a critical problem in array signal processing. Numerous methods have been proposed to estimate the number of sources…

Signal Processing · Electrical Eng. & Systems 2025-07-03 Gokularam Muthukrishnan , Siva Shanmugam , Sheetal Kalyani

We propose a method to reconstruct the optical properties of a scattering medium with subwavelength resolution. The method is based on the solution to the inverse scattering problem with photoactivated internal sources. Numerical…

Optics · Physics 2018-08-01 Anna C. Gilbert , Howard W. Levinson , John C. Schotland

The aim of this paper is to study the feasibility of time-reversal methods in a non homogeneous elastic medium, from data recorded in an acoustic medium. We aim to determine, from partial aperture boundary measurements, the presence and…

Numerical Analysis · Mathematics 2020-10-28 Franck Assous , Moshe Lin

Photoacoustic image reconstruction often assumes that the restriction of the acoustic pressure on the detection surface is given. However, commonly used detectors often have a certain directivity and frequency dependence, in which case the…

Numerical Analysis · Mathematics 2020-01-08 Gerhard Zangerl , Sunghwan Moon , Markus Haltmeier