相关论文: Unique determination of absorption coefficients in…
This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. We show…
In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of…
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…
We study the reconstruction of the attenuation and absorption coefficients in a stationary linear transport equation from knowledge of albedo operator in dimension $n\geq 3$ on a Riemannian manifold in the presence of a magnetic field. We…
We consider the inverse problem of reconstructing the optical parameters for stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales characterized by the magnitude of a…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
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…
This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from full knowledge of the albedo operator at the boundary of a bounded domain of interest. We present optimal…
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…
This paper concerns the reconstruction of the scattering coefficient in a two-dimensional transport equation from angularly averaged measurements when the probing source is isotropic and time-harmonic. This is a practical setting in the…
In this work, we prove rigorous error estimates for a hybrid method introduced in [15] for solving the time-dependent radiation transport equation (RTE). The method relies on a splitting of the kinetic distribution function for the…
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…
In this paper, we describe the numerical reconstruction method for quantitative photoacoustic tomography (QPAT) based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation…
The objective of quantitative photoacoustic tomography (QPAT) is to reconstruct optical and thermodynamic properties of heterogeneous media from data of absorbed energy distribution inside the media. There have been extensive theoretical…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
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…
Quantitative image reconstruction in photoacoustic tomography requires the solution of a coupled physics inverse problem involvier light transport and acoustic wave propagation. In this paper we address this issue employing the radiative…
We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…
We study in this work an integral formulation for the radiative transfer equation (RTE) in anisotropic media with truncated approximation to the scattering phase function. The integral formulation consists of a coupled system of integral…
We show that the inverse problems for a class of kinetic equations can be solved by classical tools in PDE analysis including energy estimates and the celebrated averaging lemma. Using these tools, we give a unified framework for the…