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We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

Analysis of PDEs · Mathematics 2026-02-24 Daniela Di Donato , Luca Rondi

This paper concerns the Bayesian approach to inverse acoustic scattering problems of inferring the position and shape of a sound-soft obstacle from phaseless far-field data generated by point source waves. To improve the convergence rate,…

Numerical Analysis · Mathematics 2021-08-23 Zhipeng Yang , Xinping Gui , Ju Ming , Guanghui Hu

We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…

Numerical Analysis · Mathematics 2018-05-22 Michael V. Klibanov , Aleksandr E. Kolesov , Dinh-Liem Nguyen

This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel…

Analysis of PDEs · Mathematics 2013-02-04 Haiwen Zhang , Bo Zhang

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

We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…

Numerical Analysis · Mathematics 2023-06-08 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

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

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…

Applications · Statistics 2011-03-14 François-Xavier Dupé , Jalal Fadili , Jean-Luc Starck

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…

A numerical method for solving the equations modeling acoustic scattering is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries…

Numerical Analysis · Mathematics 2014-06-03 Sijia Hao , Per-Gunnar Martinsson , Patrick Young

The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…

Numerical Analysis · Mathematics 2024-11-06 Nian-Ci Wu , Chengzhi Liu , Yatian Wang , Qian Zuo

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…

Analysis of PDEs · Mathematics 2023-04-05 Isaac Harris

We study an inverse scattering problem for monostatic synthetic aperture radar (SAR): Estimate the wave speed in a heterogeneous, isotropic and nonmagnetic medium probed by waves emitted and measured by a moving antenna. The forward map,…

Numerical Analysis · Mathematics 2026-01-29 Liliana Borcea , Josselin Garnier , Alexander V. Mamonov , Jörn Zimmerling

We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling…

Numerical Analysis · Mathematics 2024-07-03 J. Garnier , H. Haddar , H. Montanelli

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…

Mathematical Physics · Physics 2024-02-13 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…

Analysis of PDEs · Mathematics 2025-02-21 Zhenhao Li , Jian Wang , Jared Wunsch

The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…

Numerical Analysis · Mathematics 2018-06-18 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

The paper presents a globally convergent algorithm for solving coefficient inverse problems. Being rooted in the globally convergent numerical method (SIAM J. Sci. Comput., 31, No.1 (2008), pp. 478-509) for solving multidimensional…

Mathematical Physics · Physics 2013-08-30 Michael V. Klibanov , Alexandre Timonov

We present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing…

Numerical Analysis · Mathematics 2015-05-28 Sivaram Ambikasaran , Carlos Borges , Lise-Marie Imbert-Gerard , Leslie Greengard

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