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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…

We lay the foundations for a new fast method to reconstruct the electron density in x-ray scanning applications using measurements in the dark field. This approach is applied to a type of machine configuration with fixed energy sensitive…

Numerical Analysis · Mathematics 2015-05-08 James Webber

Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…

Mathematical Physics · Physics 2022-09-21 Jun Lai , Jinrui Zhang

This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…

Numerical Analysis · Mathematics 2023-08-14 Peijun Li , Xiaokai Yuan

We consider the scattering of time-harmonic plane waves by a compactly supported inhomogeneous scattering obstacle governed by the Helmholtz equation. Given far field observations of the scattered fields corresponding to plane wave incident…

Numerical Analysis · Mathematics 2026-02-03 Roland Griesmaier , Bastian Harrach , Jianli Xiang

We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…

Numerical Analysis · Mathematics 2022-01-14 Anton Arnold , Sjoerd Geevers , Ilaria Perugia , Dmitry Ponomarev

The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…

Computer Vision and Pattern Recognition · Computer Science 2024-07-16 Doga Dikbayir , Abdel Alsnayyan , Vishnu Naresh Boddeti , Balasubramaniam Shanker , Hasan Metin Aktulga

This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover…

Analysis of PDEs · Mathematics 2025-12-04 Chun Liu , Jiaqing Yang , Bo Zhang

More than ten years ago Ikehata discovered two mathematical methods for the purpose of extracting information about the location and shape of unknown discontinuity embedded in a known background medium from observation data. The methods are…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata

Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…

Numerical Analysis · Mathematics 2018-01-16 Daan Huybrechs , Peter Opsomer

We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…

Numerical Analysis · Mathematics 2026-02-02 Zhiqi Sun , Xiang Xu , Yiwen Lin

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

A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…

Mathematical Physics · Physics 2007-05-23 Alexander G. Ramm

Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…

Analysis of PDEs · Mathematics 2020-09-02 Jianliang Li , Jiaqing Yang , Bo Zhang

This work extends the factorization method to the inverse scattering problem of reconstructing the shape and location of an absorbing penetrable scatterer embedded in a thin infinite elastic (Kirchhoff--Love) plate. With the assumption that…

Analysis of PDEs · Mathematics 2025-11-13 Rafael Ceja Ayala , Isaac Harris , General Ozochiawaeze

In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile.…

Numerical Analysis · Mathematics 2019-01-29 Carlos Borges , George Biros

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

We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of…

Numerical Analysis · Mathematics 2025-08-18 Sarah Eberle-Blick , Bastian Harrach , Xianchao Wang

Diffraction tomography is a noninvasive technique that estimates the refractive indices of unknown objects and involves an inverse-scattering problem governed by the wave equation. Recent works have shown the benefit of nonlinear models of…

Image and Video Processing · Electrical Eng. & Systems 2021-07-09 Tao Hong , Thanh-an Pham , Eran Treister , Michael Unser

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