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We propose a method to reconstruct the density of an optical source in a highly scattering medium from ultrasound-modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the radiative…

Analysis of PDEs · Mathematics 2015-06-23 Guillaume Bal , Francis J. Chung , John C. Schotland

This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…

Analysis of PDEs · Mathematics 2020-10-28 Tilo Arens , Xia Ji , Xiaodong Liu

In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…

Analysis of PDEs · Mathematics 2024-10-02 Ru-Yu Lai , Hanming Zhou

We study the Cauchy problem for the radial energy critical nonlinear wave equation in three dimensions. Our main result proves almost sure scattering for radial initial data below the energy space. In order to preserve the spherical…

Analysis of PDEs · Mathematics 2020-06-17 Bjoern Bringmann

In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…

Analysis of PDEs · Mathematics 2013-07-30 Manabu Machida , Masahiro Yamamoto

This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…

Analysis of PDEs · Mathematics 2025-04-23 Joseph Kraisler , Wei Li , Kui Ren , John C. Schotland , Yimin Zhong

We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…

Analysis of PDEs · Mathematics 2008-03-31 Plamen Stefanov , Gunther Uhlmann

Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. This data consist of the exit directions…

Differential Geometry · Mathematics 2018-03-20 Matti Lassas , Teemu Saksala , Hanming Zhou

A photon entering a scattering medium executes a three-dimensional random walk determined by the Henyey-Greenstein phase function. The photon either reaches the boundary for a first passage or is absorbed. Projecting the walk onto the axial…

Optics · Physics 2025-12-23 Claude Zeller , Robert Cordery

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

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki , Tao Yin

We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…

Numerical Analysis · Mathematics 2018-05-23 Mirza Karamehmedović , Adrian Kirkeby , Kim Knudsen

In an ultrasonic array system, increasing the aperture size to achieve a high resolution requires more transmit and receive channels, thus making it essential to have an analysis technique that can reconstruct the shape and physical…

Optics · Physics 2025-08-21 Kai Yabumoto , Takayoshi Yumii , Kenjiro Kimura

This paper studies the reconstruction of Stekloff eigenvalues and the index of refraction of an inhomogeneous medium from Cauchy data. The inverse spectrum problem to reconstruct Stekloff eigenvalues is investigated using a new integral…

Mathematical Physics · Physics 2019-09-04 Juan Liu , Yanfang Liu , Jiguang Sun

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

Numerical Analysis · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

We propose a method to reconstruct the optical properties of a scattering medium with subwavelength resolution. The method is based on the solution to the inverse scattering problem with photoactivated internal sources. Numerical…

Optics · Physics 2018-08-01 Anna C. Gilbert , Howard W. Levinson , John C. Schotland

Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with…

Analysis of PDEs · Mathematics 2021-07-20 Ru-Yu Lai , Kui Ren , Ting Zhou

We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…

Analysis of PDEs · Mathematics 2017-10-25 Youjun Deng , Hongyu Liu , Gunther Uhlmann

In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary. We will assume that the corresponding far-field pattern is known/measured and we consider two inverse problems.…

Analysis of PDEs · Mathematics 2024-04-04 Victor Hughes , Isaac Harris , Heejin Lee

We consider the Cauchy problem for the Korteweg--de Vries equation with real initial data $q$ that is both $L^1$ and $L^2$ summable and supported on (0,\infty). Using the left reflection coefficient and Hankel operators on the Hardy space…

Mathematical Physics · Physics 2026-04-17 Alexei Rybkin