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In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the…

Analysis of PDEs · Mathematics 2021-07-20 Isaac Harris , Dinh-Liem Nguyen , Thi-Phong Nguyen

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…

Analysis of PDEs · Mathematics 2020-01-08 Xia Ji , Xiaodong Liu

This paper is concerned with the electromagnetic inverse scattering problem that aims to determine the location and shape of anisotropic scatterers from far field data (at a fixed frequency). We study the orthogonality sampling method which…

Analysis of PDEs · Mathematics 2019-11-05 Isaac Harris , Dinh-Liem Nguyen

Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to…

Machine Learning · Statistics 2024-11-14 Yazid Janati , Badr Moufad , Alain Durmus , Eric Moulines , Jimmy Olsson

This paper concerns the reconstruction of multiple elastic parameters (Lam\'e parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\mathbb{R}^2$. The direct scattering problem is…

Numerical Analysis · Mathematics 2019-02-13 Gang Bao , Tao Yin , Fang Zeng

Solution of the discretized Lippmann-Schwinger equation in the spatial frequency domain involves the inversion of a linear operator specified by the scattering potential. To regularize this inevitably ill-conditioned problem, we propose a…

Computational Physics · Physics 2020-10-30 Subeen Pang , George Barbastathis

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 work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

Numerical Analysis · Mathematics 2025-01-31 Zhiyuan Li , Chunlong Sun , Xiangcheng Zheng

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward…

Signal Processing · Electrical Eng. & Systems 2024-02-29 Joshua R. Tempelman , Tobias Weidemann , Eric B. Flynn , Kathryn H. Matlack , Alexander F. Vakakis

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

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

Methodology · Statistics 2023-02-09 Xiao Liu , Kyongmin Yeo

We propose an end-to-end approach for solving inverse problems for a class of complex astronomical signals, namely Spectral Energy Distributions (SEDs). Our goal is to reconstruct such signals from scarce and/or unreliable measurements. We…

Instrumentation and Methods for Astrophysics · Physics 2020-12-14 Agapi Rissaki , Orestis Pavlou , Dimitris Fotakis , Vicky Papadopoulou , Andreas Efstathiou

In this paper we discuss inverse medium problems. We develop the direct sampling method based on probing indices using the saddle point formulation. The medium is constructed by solutions of saddle point problems. The method improves the…

Numerical Analysis · Mathematics 2024-12-31 Kazufumi Ito

We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…

Analysis of PDEs · Mathematics 2024-12-20 Alexander Konschin , Armin Lechleiter

Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…

Computer Vision and Pattern Recognition · Computer Science 2024-12-31 Shayan Mohajer Hamidi , En-Hui Yang

The direct and inverse scattering problems are analyzed for a first-order discrete system associated with the semi-discrete version of the derivative NLS system. The Jost solutions, the scattering coefficients, the bound-state dependency…

Mathematical Physics · Physics 2022-03-08 T. Aktosun , R. Ercan

The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a linear integral equation called…

Numerical Analysis · Mathematics 2022-03-16 Timo Lähivaara , Peter Monk , Virginia Selgas

Solving electromagnetic inverse scattering problems (ISPs) is challenging due to the intrinsic nonlinearity, ill-posedness, and expensive computational cost. Recently, deep neural network (DNN) techniques have been successfully applied on…

Machine Learning · Computer Science 2021-11-18 Zicheng Liu , Mayank Roy , Dilip K. Prasad , Krishna Agarwal

This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…

Mathematical Physics · Physics 2016-11-02 Howard W. Levinson , Vadim A. Markel

In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…

Numerical Analysis · Mathematics 2020-10-28 Carlos Borges , Jun Lai