English
Related papers

Related papers: Unique determination by a single far-field measure…

200 papers

We prove a new uniqueness theorem for an inverse scattering problem without the phase information for the 3-D Helmholtz equation. The spatially distributed dielectric constant is the subject of the interest in this problem. We consider the…

Mathematical Physics · Physics 2017-01-03 Michael V. Klibanov

Motivated by applications in quantitative photoacoustic imaging, we study inverse problems to a semilinear radiative transport equation (RTE) where we intend to reconstruct absorption coefficients in the equation from single and multiple…

Analysis of PDEs · Mathematics 2020-07-21 Kui Ren , Yimin Zhong

Motivated by non-destructive testing of optical fiber, we consider the problem of determining the index of refraction of a two-dimensional medium from magnitude of the total field resulting from known incident plane waves at a fixed…

Analysis of PDEs · Mathematics 2016-08-01 Yat Tin Chow , Fadil Santosa , Gunther Uhlmann

This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape…

Numerical Analysis · Mathematics 2022-02-21 Deyue Zhang , Yue Wu , Yinglin Wang , Yukun Guo

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Analysis of PDEs · Mathematics 2017-06-15 Jingzhi Li , Xiaofei Li , Hongyu Liu

The recovery of anomalies from backscattering far field data is a long-standing open problem in inverse scattering theory. We make a first step in this direction by establishing the unique identifiability of convex impenetrable obstacles…

Numerical Analysis · Mathematics 2025-12-29 Jialei Li , Xiaodong Liu , Qingxiang Shi

For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…

Numerical Analysis · Mathematics 2018-05-24 Andrew Gibbs , Stephen Langdon , Andrea Moiola

We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the…

Analysis of PDEs · Mathematics 2015-02-05 Jingzhi Li , Hongyu Liu

Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…

Disordered Systems and Neural Networks · Physics 2014-10-09 Hui Khoon Ng , Berthold-Georg Englert

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 scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave…

Analysis of PDEs · Mathematics 2012-10-12 Roland Griesmaier , Nuutti Hyvönen , Otto Seiskari

We are concerned with the linearized, isotropic and homogeneous elastic scattering problem by (possibly many) small rigid obstacles of arbitrary Lipschitz regular shapes in 3D. Based on the Foldy-Lax approximation, valid under a sufficient…

Analysis of PDEs · Mathematics 2016-10-20 Fadhel Al-Musallam , Durga Prasad Challa , Mourad Sini

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…

Analysis of PDEs · Mathematics 2015-05-18 Xiaodong Liu , Bo Zhang , Jiaqing Yang

In this paper we investigate the possibility of modeling a single antenna alone and in close proximity to a physical object by means of discrete point source scatterers. The scatter point model allows joint modeling of a physical antenna…

Signal Processing · Electrical Eng. & Systems 2021-03-26 Thomas Wilding , Erik Leitinger , Ulrich Muehlmann , Klaus Witrisal

We study an inverse uniqueness with a knowledge of spectral data in the interior transmission problem defined by an index of refraction in a simple domain. We expand the solution in such a domain into a series of one dimensional problems.…

Analysis of PDEs · Mathematics 2015-08-10 Lung-Hui Chen

We consider the solvability of the direct scattering problem of an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. We prove the existence and uniqueness…

Analysis of PDEs · Mathematics 2024-02-23 Drossos Gintides , Sotiris Giogiakas , Leonidas Mindrinos

We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for the finite dimensional zero-finding problem of a continuously differentiable, pointwise convex and monotonic function.…

Numerical Analysis · Mathematics 2022-12-13 Bastian Harrach

In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of one-dimensional reaction-diffusion equations. Such reaction-diffusion equations include the classical model of…

Analysis of PDEs · Mathematics 2011-05-30 Michel Cristofol , Jimmy Garnier , Francois Hamel , Lionel Roques

This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…

Analysis of PDEs · Mathematics 2019-09-04 Peijun Li , Jue Wang , Lei Zhang