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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 study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…

Analysis of PDEs · Mathematics 2026-04-21 Kui Ren , Yimin Zhong

We consider the inverse problem of reconstructing the scattering coefficient of a simple radiative transport equation (RTE) used to model light propagation inside a scattering medium. To do so, we extract information from the second term in…

Analysis of PDEs · Mathematics 2025-08-07 Francis Chung , Faith Hensley

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 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

This work studies the inverse boundary problem for the two photon absorption radiative transport equation. We show that the absorption coefficients and scattering coefficients can be uniquely determined from the \emph{albedo} operator. If…

Analysis of PDEs · Mathematics 2022-02-21 Plamen Stefanov , Yimin Zhong

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…

Numerical Analysis · Mathematics 2017-08-08 Qin Li , Ruiwen Shu , Li Wang

We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption "a" and the scattering coefficient "k" are to be recovered from the albedo operator. We show that "gauge equivalent" pairs…

Analysis of PDEs · Mathematics 2008-09-16 Plamen Stefanov , Alexandru Tamasan

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 consider the classical integral equation reformulation of the radiative transport equation (RTE) in a heterogeneous medium, assuming isotropic scattering. We prove an estimate for the norm of the integral operator in this formulation…

Numerical Analysis · Mathematics 2019-03-21 J. C. H. Blake , I. G. Graham , F. Scheben , A. Spence

We consider an inverse problem for a radiative transport equation (RTE) in which boundary sources and measurements are restricted to a single subset $E$ of the boundary of the domain $\Omega$. We show that this problem can be solved…

Analysis of PDEs · Mathematics 2020-01-31 Francis J. Chung

A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the…

Mathematical Physics · Physics 2007-05-23 George Panasyuk , John C. Schotland , Vadim A. Markel

We consider the inverse problem of recovering the optical properties of a highly-scattering medium from acousto-optic measurements. Using such measurements, we show that the scattering and absorption coefficients of the radiative transport…

Analysis of PDEs · Mathematics 2016-09-27 Francis J Chung , John C Schotland

An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence…

Numerical Analysis · Mathematics 2022-06-24 Michael V. Klibanov , Jingzhi Li , Loc H. Nguyen , Zhipeng Yang

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 demonstrate that simultaneous reconstruction of scattering and absorption of a mesoscopic system using angularly-resolved measurements of scattered light intensity is possible. Image reconstruction is realized based on the algebraic…

Optics · Physics 2011-01-07 Lucia Florescu , John C. Schotland , Vadim A. Markel

We study the stability of the reconstruction of the scattering and absorption coefficients in a stationary linear transport equation from knowledge of the full albedo operator in dimension $n\geq3$. The albedo operator is defined as the…

Mathematical Physics · Physics 2009-02-19 Guillaume Bal , Alexandre Jollivet

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 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

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
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