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Related papers: Inverse Transport and Acousto-Optic Imaging

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In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown…

Analysis of PDEs · Mathematics 2015-03-30 Sebastian Acosta

We consider an inverse transport problem in fluorescence ultrasound modulated optical tomography (fUMOT) with angularly averaged illuminations and measurements. We study the uniqueness and stability of the reconstruction of the absorption…

Mathematical Physics · Physics 2020-02-19 Wei Li , Yang Yang , Yimin Zhong

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

Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…

Numerical Analysis · Mathematics 2015-06-19 Tian Ding , Kui Ren

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the…

Mathematical Physics · Physics 2015-05-14 Guillaume Bal , Alexandre Jollivet , Vincent Jugnon

We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, the exiting radiation is measured on an arc. The attenuation and scattering…

Analysis of PDEs · Mathematics 2021-11-17 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…

We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…

Numerical Analysis · Mathematics 2017-08-11 Ke Chen , Qin Li , Li Wang

We propose a method to reconstruct the electrical current density inside a conducting medium from acoustically-modulated boundary measurements of the electric potential. We show that the current can be uniquely reconstructed with Lipschitz…

Analysis of PDEs · Mathematics 2021-03-23 Wei Li , John C. Schotland , Yang Yang , Yimin Zhong

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

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 concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…

Numerical Analysis · Mathematics 2015-06-19 Thorsten Hohage , Frederic Weidling

We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…

Analysis of PDEs · Mathematics 2024-10-31 Safiere Kuijpers , Laura Scarabosio

We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a…

Analysis of PDEs · Mathematics 2024-05-13 Ru-Yu Lai , Gunther Uhlmann , Hanming Zhou

We study the inverse problem in Optical Tomography of determining the optical properties of a medium $\Omega\subset\mathbb{R}^n$, with $n\geq 3$, under the so-called diffusion approximation. We consider the time-harmonic case where $\Omega$…

Analysis of PDEs · Mathematics 2020-05-11 Olga Doeva , Romina Gaburro , William R. B. Lionheart , Clifford J. Nolan

This paper concerns the quantitative step of the medical imaging modality Thermo-acoustic Tomography (TAT). We model the radiation propagation by a system of Maxwell's equations. We show that the index of refraction of light and the…

Analysis of PDEs · Mathematics 2015-06-17 Guillaume Bal , Ting Zhou

We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…

Numerical Analysis · Mathematics 2023-06-08 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove…

Analysis of PDEs · Mathematics 2018-01-17 L. Beilina , M. Cristofol , S. Li , M. Yamamoto

The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption…

Analysis of PDEs · Mathematics 2014-03-25 Habib Ammari , Josselin Garnier , Loc Hoang Nguyen , Laurent Seppecher

We consider the inverse problem of reconstructing the optical parameters of the radiative transfer equation (RTE) from boundary measurements in the diffusion limit. In the diffusive regime (the Knudsen number $\mathsf{Kn}\ll 1$), the…

Analysis of PDEs · Mathematics 2018-08-08 Ru-Yu Lai , Qin Li , Gunther Uhlmann