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In this paper we develop a numerical method for solving an inverse scattering problem of estimating the scattering potential in a Schr\"{o}dinger equation from frequency domain measurements based on reduced order models (ROM). The ROM is a…

Numerical Analysis · Mathematics 2025-11-10 Andreas Tataris , Tristan van Leeuwen , Alexander V. Mamonov

The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the…

Numerical Analysis · Mathematics 2020-04-16 Alexey Smirnov , Michael Klibanov , Anders Sullivan , Lam Nguyen

This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…

Analysis of PDEs · Mathematics 2020-10-28 Tilo Arens , Xia Ji , Xiaodong Liu

In this paper we investigate spectral properties of the damped elastic wave equation. Deducing a correspondence between the eigenvalue problem of this model and the one of Lam\'e operators with non self-adjoint perturbations, we provide…

Spectral Theory · Mathematics 2021-08-18 Biagio Cassano , Lucrezia Cossetti , Luca Fanelli

Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…

Analysis of PDEs · Mathematics 2020-12-15 Tielei Zhu , Jiaqing Yang

Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…

Numerical Analysis · Mathematics 2015-06-19 Tian Ding , Kui Ren

This paper concerns an inverse band structure problem for one dimensional periodic Schr\"odinger operators (Hill's operators). Our goal is to find a potential for the Hill's operator in order to reproduce as best as possible some given…

Optimization and Control · Mathematics 2017-09-22 Athmane Bakhta , Virginie Ehrlacher , David Gontier

We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far…

Numerical Analysis · Mathematics 2017-04-05 Roland Griesmaier , Christian Schmiedecke

A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…

Analysis of PDEs · Mathematics 2007-05-23 Kenrick Bingham , Yaroslav Kurylev , Matti Lassas , Samuli Siltanen

We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed and nonlinear, and the iterative…

Analysis of PDEs · Mathematics 2022-08-31 Takashi Furuya , Roland Potthast

This paper is concerned with the inverse acoustic scattering problems of reconstructing time-dependent multiple point sources and sources on a curve $L$ of the form $\lambda(t)\tau(x)\delta_L(x)$. A direct sampling method with a novel…

Numerical Analysis · Mathematics 2023-09-07 Jiaru Wang , Bo Chen , Qingqing Yu , Yao Sun

In this article, the inverse scattering problem (ISP) of recovering the matrix coefficient of a first order system of ordinary differential equations on the half-axis from its scattering matrix is considered. In the case of a triangular…

Spectral Theory · Mathematics 2013-07-02 Mansur I. Ismailov

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 suggest a new statement of the inverse spectral problem for Sturm--Liouville-type operators with constant delay. This inverse problem consists in recovering the coefficient (often referred to as potential) of the delayed term in the…

Spectral Theory · Mathematics 2023-04-13 Sergey Buterin , Sergey Vasilev

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

Numerical Analysis · Mathematics 2016-10-06 Giovanni S. Alberti , Habib Ammari , Bangti Jin , Jin-Keun Seo , Wenlong Zhang

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Numerical Analysis · Mathematics 2020-02-03 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky , Jörn Zimmerling

In this paper we study a Cauchy problem for the nonlinear damped wave equations for a general positive operator with discrete spectrum. We derive the exponential in time decay of solutions to the linear problem with decay rate depending on…

Analysis of PDEs · Mathematics 2017-12-15 Michael Ruzhansky , Niyaz Tokmagambetov

We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…

Numerical Analysis · Mathematics 2024-08-21 Andrea Aspri , Leon Frischauf , Otmar Scherzer

A novel formulation of the hyperspectral broadband phase retrieval is developed for the scenario where both object and modulation phase masks are spectrally varying. The proposed algorithm is based on a complex domain version of the…

Image and Video Processing · Electrical Eng. & Systems 2021-05-18 Vladimir Katkovnik , Igor Shevkunov , Karen Egiazarian

This paper presents a novel method for recovering sparse vectors from linear models corrupted by Poisson noise. The contribution is twofold. First, an operator defined via the external division of two Bregman proximity operators is…

Machine Learning · Computer Science 2026-02-13 Kazuki Haishima , Kyohei Suzuki , Konstantinos Slavakis