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This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…

Analysis of PDEs · Mathematics 2026-04-14 Jialei Li , Xiaodong Liu

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

We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…

Mathematical Physics · Physics 2026-05-25 John C. Schotland , Shenwen Yu

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…

Analysis of PDEs · Mathematics 2012-10-22 G. Giorgi , M. Brignone , R. Aramini , M. Piana

This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…

Analysis of PDEs · Mathematics 2018-12-26 Alexey Agaltsov , Thorsten Hohage , Roman Novikov

A version of the so-called "convexification" numerical method for a coefficient inverse scattering problem for the 3D Hemholtz equation is developed analytically and tested numerically. Backscattering data are used, which result from a…

Numerical Analysis · Mathematics 2018-01-16 Michael V. Klibanov , Aleksandr E. Kolesov

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…

Analysis of PDEs · Mathematics 2017-11-02 Li Jingzhi , Liu Hongyu , Sun Hongpeng

This paper is concerned with the numerical solution to a 3D coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are associated with a single direction of an incident plane wave,…

Numerical Analysis · Mathematics 2017-05-04 Dinh-Liem Nguyen , Michael V. Klibanov , Loc H. Nguyen , Michael A. Fiddy

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…

Analysis of PDEs · Mathematics 2019-06-07 Xia Ji , Xiaodong Liu

In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…

Numerical Analysis · Mathematics 2023-10-16 Abinand Gopal , Jeremy Hoskins , Vladimir Rokhlin

An inverse problem of acoustic sounding is under consideration in a form of 3D inverse coefficient problem for wave equation. Unknown coefficient is the local propagation velocity of vibrations, which is associated with inhomogeneities of…

Numerical Analysis · Mathematics 2017-03-06 A. S. Leonov , A. B. Bakushinsky

Due to manufacturing defects or wear and tear, industrial components may have uncertainties. In order to evaluate the performance of machined components, it is crucial to quantify the uncertainty of the scattering surface. This brings up an…

Numerical Analysis · Mathematics 2025-04-28 Yi Wang , Lei Lin , Junliang Lv

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 quantum and acoustic wave propagation at fixed frequency for compactly supported scatterers in dimension $d\ge 2$. In these framework we give explicit formulas for phase recovering from appropriate phaseless scattering data. As…

Mathematical Physics · Physics 2015-02-17 Roman Novikov

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

We consider the inverse scattering problem for inhomogeneous media of compact support governed by the fractional s-Helmholtz equation, with $0<s<1$, in dimensions $d=1,2,3$. In particular, we study the determination of the support of the…

Analysis of PDEs · Mathematics 2026-04-30 Dana Zilberberg

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

Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…

Analysis of PDEs · Mathematics 2018-08-08 Xia Ji , Xiaodong Liu , Bo Zhang

This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…

Inverse scattering problems without the phase information arise in imaging of nanostructures whose sizes are hundreds of nanometers as well as in imaging of biological cells. The governing equation is the 3-d generalized Helmholtz equation…

Analysis of PDEs · Mathematics 2015-10-05 Michael V. Klibanov , Loc H. Nguyen , Kejia Pan