English
Related papers

Related papers: Reduced Order Model Approach to Inverse Scattering

200 papers

We introduce a novel nonlinear imaging method for the acoustic wave equation based on data-driven model order reduction. The objective is to image the discontinuities of the acoustic velocity, a coefficient of the scalar wave equation from…

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

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…

Computational Engineering, Finance, and Science · Computer Science 2017-09-01 Emmanuel Soubies , Thanh-An Pham , Michael Unser

A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…

Numerical Analysis · Mathematics 2019-04-02 Alexey V. Smirnov , Michael V. Klibanov , Loc H. Nguyen

Waveform inversion is concerned with estimating a heterogeneous medium, modeled by variable coefficients of wave equations, using sources that emit probing signals and receivers that record the generated waves. It is an old and intensively…

Numerical Analysis · Mathematics 2024-10-29 Liliana Borcea , Josselin Garnier , Alexander V. Mamonov , Jörn Zimmerling

The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging to…

Optics · Physics 2021-09-08 Moosung Lee , Herve Hugonnet , YongKeun Park

We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…

Analysis of PDEs · Mathematics 2020-01-08 Hongyu Liu , Xiaodong Liu , Xianchao Wang , Yuliang Wang

Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…

Numerical Analysis · Mathematics 2020-07-14 Selin Aslan , Eric de Sturler , Serkan Gugercin

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical…

Numerical Analysis · Mathematics 2019-11-19 Giovanni Stabile , Bojana Rosic

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

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…

Analysis of PDEs · Mathematics 2011-01-24 Tim J. P. M. Op 't Root , Christiaan C. Stolk , Maarten V. de Hoop

In this paper, we study the inverse scattering problem for a class of signals that have a compactly supported reflection coefficient. The problem boils down to the solution of the Gelfand-Levitan-Marchenko (GLM) integral equations with a…

Computational Physics · Physics 2019-02-12 Vishal Vaibhav

We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…

Mathematical Physics · Physics 2016-07-18 Liliana Borcea , Ilker Kocyigit

An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…

Numerical Analysis · Mathematics 2014-04-30 Ying Li

In this paper, we study an inverse scattering problem at fixed energy on three-dimensional asymptotically hyperbolic St{\"a}ckel manifolds having the topology of toric cylinders and satisfying the Robertson condition. On these manifolds the…

Analysis of PDEs · Mathematics 2016-05-18 Damien Gobin

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…

Mathematical Physics · Physics 2007-05-23 S. Gutman , A. G. Ramm , W. Scheid

This paper addresses the inverse scattering problem in the domain Omega. The input data, measured outside Omega, involve the waves generated by the interaction of plane waves with various directions and unknown scatterers fully occluded…

Numerical Analysis · Mathematics 2024-06-25 Phuong M. Nguyen , Loc H. Nguyen , Huong T. T. Vu

Inverse wave scattering aims at determining the properties of an object using data on how the object scatters incoming waves. In order to collect information, sensors are put in different locations to send and receive waves from each other.…

Machine Learning · Computer Science 2026-01-22 Hanyang Jiang , Yuehaw Khoo , Haizhao Yang

A large number of theoretically predicted waveforms are required by matched-filtering searches for the gravitational-wave signals produced by compact binary coalescence. In order to substantially alleviate the computational burden in…

General Relativity and Quantum Cosmology · Physics 2018-06-11 Dániel Barta , Mátyás Vasúth

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

Inverse scattering aims to infer information about a hidden object by using the received scattered waves and training data collected from forward mathematical models. Recent advances in computing have led to increasing attention towards…

Applications · Statistics 2023-05-03 Chih-Li Sung , Yao Song , Ying Hung