English
Related papers

Related papers: Multifrequency inverse obstacle scattering with un…

200 papers

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…

Machine Learning · Computer Science 2025-07-09 Wenjin Qin , Hailin Wang , Jingyao Hou , Jianjun Wang

This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover…

Analysis of PDEs · Mathematics 2021-12-24 Yan Chang , Yukun Guo

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

In this paper, we give a positive answer to a challenging open problem for recovering unknown obstacle (which is usually referred to as a scatterer) by acoustic wave probe associated to the Helmholtz equation. We show that the acoustic…

Analysis of PDEs · Mathematics 2021-04-20 Genqian Liu

In a medium where the dielectric permittivity is perturbed in the presence of an acoustic wave, optical scattering generates frequency-shifted light. In this paper we consider the inverse problem of recovering the optical properties of this…

Analysis of PDEs · Mathematics 2019-10-14 Francis J. Chung , Jeremy G. Hoskins , John C. Schotland

We describe a new algorithm to solve a particular phase retrieval problem, that has wide applications in audio processing: the reconstruction of a function from its scalogram, that is from the modulus of its wavelet transform. It is a…

Optimization and Control · Mathematics 2017-04-11 Irène Waldspurger

Reconstructions of potential in Schrodinger equation with data in the diffusion frequency domain have been successfully obtained within Lippmann-Schwinger-Lanczos (LSL) approach, however limited resolution away from the sensor positions…

Numerical Analysis · Mathematics 2025-04-08 Anarzhan Abilgazy , Mikhail Zaslavskiy

We consider boundary measurements for the wave equation on a bounded domain $M \subset \R^2$ or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an…

Analysis of PDEs · Mathematics 2011-06-17 Lauri Oksanen

Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…

Computer Vision and Pattern Recognition · Computer Science 2018-07-04 Yu Sun , Zhihao Xia , Ulugbek S. Kamilov

Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group…

Statistics Theory · Mathematics 2022-03-11 Subhro Ghosh , Philippe Rigollet

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

Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is…

Computer Vision and Pattern Recognition · Computer Science 2024-11-05 Zachary H. Hendrix , Peter T. Brown , Tim Flanagan , Douglas P. Shepherd , Ayush Saurabh , Steve Pressé

Reconstructing an object's shape and appearance in terms of a mesh textured by a spatially-varying bidirectional reflectance distribution function (SVBRDF) from a limited set of images captured under collocated light is an ill-posed…

Computer Vision and Pattern Recognition · Computer Science 2025-01-31 Julian Kaltheuner , Patrick Stotko , Reinhard Klein

The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical methods suffer from prohibitive computational costs, while…

Mathematical Physics · Physics 2025-10-13 Xinwei Hu , Jingrun Chen , Haijun Yu

We consider the unique determinations of impenetrable obstacles or diffraction grating profiles in $\mathbb{R}^3$ by a single far-field measurement within polyhedral geometries. We are particularly interested in the case that the scattering…

Analysis of PDEs · Mathematics 2021-11-30 Xinlin cao , Huaian Diao , Hongyu Liu , Jun Zou

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Numerical Analysis · Mathematics 2022-03-14 Lu Zhao , Heping Dong , Fuming Ma

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

Multireference alignment (MRA) refers to the problem of recovering a signal from noisy samples subject to random circular shifts. Expectation--maximization (EM) and variational approaches use statistical modeling to achieve high accuracy at…

Information Theory · Computer Science 2025-10-30 Vahid Shahverdi , Emanuel Ström , Joakim Andén

Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the Lipschitz boundary of a bounded obstacle…

Analysis of PDEs · Mathematics 2020-06-15 Andrea Mantile , Andrea Posilicano