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Related papers: A Two-stage Method for Inverse Medium Scattering

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Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…

Analysis of PDEs · Mathematics 2025-06-02 Chun Liu , Guanghui Hu , Tao Yin , Bo Zhang

Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…

Image and Video Processing · Electrical Eng. & Systems 2024-12-23 Matthias M. Saurer , Han Na , Marius Brinkmann , Thomas F. Eibert

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 work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…

Numerical Analysis · Mathematics 2023-10-13 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang

Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping optics, and the highly nonlinear…

Computational Physics · Physics 2021-06-02 Philipp M Pelz , Hamish G Brown , Jim Ciston , Scott D Findlay , Yaqian Zhang , Mary Scott , Colin Ophus

Multiple light scattering hampers imaging objects in complex scattering media. Approaches used in real practices mainly aim to filter out multiple scattering obscuring the ballistic waves that travel straight through the scattering medium.…

A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…

Numerical Analysis · Mathematics 2024-10-18 Jiachuan Cao , Buyang Li , Yanping Lin , Fangyan Yao

The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…

Optics · Physics 2009-09-15 Albert C. Fannjiang

The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…

Numerical Analysis · Mathematics 2020-04-15 Abinash Nayak

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…

Numerical Analysis · Mathematics 2024-04-24 Fatemeh P. A. Beik , Michele Benzi , Mehdi Najafi-Kalyani

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

We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an…

Optimization and Control · Mathematics 2018-01-09 Damek Davis , Dmitriy Drusvyatskiy , Courtney Paquette

Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the…

Numerical Analysis · Mathematics 2017-06-22 Jun Lai , Ming Li , Peijun Li , Wei Li

We apply adaptive sensing techniques to the problem of locating sparse metallic scatterers using high-resolution, frequency modulated continuous wave W-band RADAR. Using a single detector, a frequency stepped source, and a lateral…

We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…

Numerical Analysis · Mathematics 2019-03-27 Anna C. Gilbert , Howard W. Levinson , John C. Schotland

This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the…

Numerical Analysis · Mathematics 2021-07-02 Xiaodong Liu , Shixu Meng , Bo Zhang

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…

Numerical Analysis · Mathematics 2025-02-25 Yun Zhang , Xiaoli Feng , Xiongbin Yan

We consider the inverse problem of determining the fragmentation rate from noisy measurements in the growth-fragmentation equation. We use Fourier transform theory on locally compact groups to treat this problem for general fragmentation…

Numerical Analysis · Mathematics 2024-02-20 Alvaro Almeida Gomez , Jorge Zubelli

Inverse scattering is a fundamental challenge in many imaging applications, ranging from microscopy to remote sensing. Solving this problem often requires jointly estimating two unknowns -- the image and the scattering field inside the…

Image and Video Processing · Electrical Eng. & Systems 2025-05-21 Yuan Gao , Wenhan Guo , Yu Sun

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