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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

Consider the inverse scattering of time-harmonic acoustic scattering by an infinite rough surface which is supposed to be a local perturbation of a plane. A novel version of reverse time migration (RTM) is proposed to reconstruct the shape…

Analysis of PDEs · Mathematics 2023-10-24 Jianliang Li , Hao Wu , Jiaqing Yang

Regularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of…

Functional Analysis · Mathematics 2016-05-05 Gitta Kutyniok , Volker Mehrmann , Philipp Petersen

This paper investigates the inverse scattering problem of recovering a sound-soft obstacle using passive measurements taken from randomly distributed point sources. The randomness introduced by these sources poses significant challenges,…

Numerical Analysis · Mathematics 2024-07-08 Yunwen Yin , Liang Yan

This work is dedicated to uniqueness and numerical algorithms for determining the point sources of the biharmonic wave equation using scattered fields at sparse sensors. We first show that the point sources in both $\mathbb{R}^2$ and…

Analysis of PDEs · Mathematics 2025-03-11 Xiaodong Liu , Qingxiang Shi , Jing Wang

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

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…

Numerical Analysis · Mathematics 2020-02-25 Trung Truong , Dinh-Liem Nguyen , Michael Klibanov

We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the…

Numerical Analysis · Mathematics 2022-09-20 Yanfang Liu , Zhizhang Wu , Jiguang Sun , Zhiwen Zhang

Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…

Analysis of PDEs · Mathematics 2025-11-06 Thorsten Hohage , Meng Liu

The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…

Data Analysis, Statistics and Probability · Physics 2009-05-19 Albert Fannjiang , Pengchong Yan , Thomas Strohmer

In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…

Analysis of PDEs · Mathematics 2019-11-27 Peijun Li , Xu Wang

We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…

Analysis of PDEs · Mathematics 2025-09-18 Nana Meng

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

We study the time-harmonic scattering by a heterogeneous object covered with a thin layer of randomly distributed sound-soft nanoparticles. The size of the particles, their distance between each other and the layer's thickness are all of…

Analysis of PDEs · Mathematics 2026-01-13 Amandine Boucart , Sonia Fliss , Laure Giovangigli

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

Analysis of PDEs · Mathematics 2016-08-10 Gang Bao , Chuchu Chen , Peijun Li

We consider the acoustic source imaging problems using multiple frequency data. Using the data of one observation direction/point, we prove that some information (size and location) of the source support can be recovered. A non-iterative…

Analysis of PDEs · Mathematics 2017-12-08 Ala Alzaalig , Guanghui Hu , Xiaodong Liu , Jiguang Sun

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…

Numerical Analysis · Mathematics 2018-12-18 J. Tanner Slagel , Julianne Chung , Matthias Chung , David Kozak , Luis Tenorio

We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance and transmission boundary conditions. In particular, we aim to quantify diffracted fields…

Numerical Analysis · Mathematics 2020-02-13 Paul Escapil-Inchauspé , Carlos Jerez-Hanckes

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…

Numerical Analysis · Mathematics 2018-04-17 Xiaoli Liu , Bo Zhang , Haiwen Zhang