English
Related papers

Related papers: A theoretical and computational framework for thre…

200 papers

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

Analysis of PDEs · Mathematics 2017-09-07 Peijun Li , Xiaokai Yuan

We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is…

Numerical Analysis · Mathematics 2024-12-20 Thanh T. Nguyen , Michael V. Klibanov

We present a new framework for the analysis and design of randomized algorithms for solving various types of linear systems, including consistent or inconsistent, full rank or rank-deficient. Our method is formulated with four randomized…

Optimization and Control · Mathematics 2022-08-25 Deren Han , Jiaxin Xie

We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…

Analysis of PDEs · Mathematics 2013-10-15 Guanghui Hu , Jingzhi Li , Hongyu Liu , Hongpeng Sun

This paper proposes a data-driven method to solve the fixed-energy inverse scattering problem for radially symmetric potentials using radial basis function (RBF) neural networks in an open-loop control system. The method estimates the…

Nuclear Theory · Physics 2026-02-09 Gábor Balassa

This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…

Analysis of PDEs · Mathematics 2021-02-16 Jianliang Li , Peijun Li , Xu Wang

In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…

Numerical Analysis · Mathematics 2015-06-22 Jun Lai , Motoki Kobayashi , Leslie Greengard

We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…

Optics · Physics 2012-08-23 Johannes Skaar , Magnus W. Haakestad

We present a novel inverse rendering-based framework to estimate the 3D shape (per-pixel surface normals and depth) of objects and scenes from single-view polarization images, the problem popularly known as Shape from Polarization (SfP).…

Computer Vision and Pattern Recognition · Computer Science 2024-07-15 Ashish Tiwari , Shanmuganathan Raman

We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering…

Analysis of PDEs · Mathematics 2020-01-29 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Optimization and Control · Mathematics 2021-06-08 Yong Sheng Soh , Venkat Chandrasekaran

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

An approach is presented for the inversion of simulated and experimental in-plane, co-polarized light scattering data in p and s polarization to obtain the normalized surface-height autocorrelation function and the rms-roughness of a…

Optics · Physics 2024-06-13 I. Simonsen , J. B. Kryvi , A. A. Maradudin

We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropriate rescaling, is used as a regularization parameter within…

Numerical Analysis · Mathematics 2026-03-02 Victor Chenu , Houssem Haddar , Hadrien Montanelli

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…

Numerical Analysis · Mathematics 2015-07-07 Alessio Spantini , Antti Solonen , Tiangang Cui , James Martin , Luis Tenorio , Youssef Marzouk

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

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

Analysis of PDEs · Mathematics 2025-07-02 Jianliang Li , Peijun Li , Xu Wang , Guanlin Yang

A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…

Numerical Analysis · Mathematics 2023-07-28 Yannik G. Gleichmann , Marcus J. Grote

A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…

Analysis of PDEs · Mathematics 2017-12-08 Huaian Diao , Peijun Li , Xiaokai Yuan

We develop the d-bar approach to inverse scattering at fixed energy in dimensions $d\ge 3$ of [Beals, Coifman 1985] and [Henkin, Novikov 1987]. As a result we propose a stable method for nonlinear approximate finding a potential $v$ from…

Mathematical Physics · Physics 2007-05-23 Roman Novikov