光声逆输运理论

Unique determination of absorption coefficients in a semilinear transport equation

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 internal data sets. We derive uniqueness and stability results for the inverse transport problem in the absence of scattering (in which case we also derive some explicit reconstruction methods) and in the presence of known scattering.

周期性通道中的扩散诱导输运及其反问题

Diffusion's induced transport in periodic channels and an inverse problem

在一维几何条件下，对周期边界条件下的Fokker-Plank方程的线性模型定义了扩散诱导输运。流动是由扩散和由速度势引起的周期性导出力产生的。一个反问题，建议用于评估的派生力的响应函数与流量。在一定的简化假设下，反问题可以部分求解。

Quantitative PAT with simplified $P_N$ approximation

The photoacoustic tomography (PAT) is a hybrid modality that combines the optics and acoustics to obtain high resolution and high contrast imaging of heterogeneous media. In this work, our objective is to study the inverse problem in the quantitative step of PAT which aims to reconstruct the optical coefficients of the governing radiative transport equation from the ultrasound measurements. In our analysis, we take the simplified $P_N$ approximation of the radiative transport equation as the physical model and then show the uniqueness and stability for this modified inverse problem. Numerical …

含时逆输运的稳定性

Stability for time-dependent inverse transport

本文研究了在有界区域边界上，由充分的知识重构含时线性输运方程中的吸收和散射参数.我们提出了最佳的稳定性结果的重建的吸收和散射参数的测量中的一个给定的错误的Adjudo运营商。

平稳逆迁移的稳定性估计

Stability estimates in stationary inverse transport

本文从$n\geq3$维的全隐式算子出发，研究了稳态线性输运方程中散射系数和吸收系数重构的稳定性。在紧致凸区域的边界上，将输入边界条件映射到输出输运解，定义了一种新的输运算子。文[M. Choulli-P. Stefanov，1996和1999]，并在[J. N. Wang，1999]，用于空间独立的散射系数。我们推广了这些结果，并证明了空间相关的散射系数的$L^1$稳定性估计。

含时角平均逆输运

Time-dependent angularly averaged inverse transport

本文涉及的吸收和散射参数的重建与时间有关的线性输运方程的知识进行角平均测量在边界的一个域的利益。我们表明，吸收系数和散射系数的空间分量是唯一确定的这样的测量。我们得到的吸收和散射参数的重建相对于测量的Escherido运营商的稳定性结果。通过将测量值精确分解为在时域中具有不同奇异行为的分量来获得稳定性结果。

Inverse transport problem in fluorescence ultrasound modulated optical tomography with angularly averaged measurements

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 coefficient and the quantum efficiency of the fluorescent probes. Reconstruction algorithms are proposed and numerical validations are performed as well. This paper is an extension of arXiv:1804.01135, where a diffusion model for this problem was considered.

Instability of an inverse problem for the stationary radiative transport near the diffusion limit

In this work, we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit, i.e. the normalized mean free path (the Knudsen number) $0 < \eps \ll 1$. It is well-known that there is a transition of stability from Hölder type to logarithmic type with $\eps\to 0$, the theory of this transition of stability is still an open problem. In this study, we show the transition of stability by establishing the balance of two different regimes depending on the relative sizes of $\eps$ and the perturbation in measurements. When $…

辐射输运的时间反演及其在逆问题和控制问题中的应用

Time reversal for radiative transport with applications to inverse and control problems

在本文中，我们开发了一个时间反演方法的辐射输运方程来解决两个问题：从边界测量的初始条件的恢复的反问题，和有限的转向时间的传输场的精确边界可控性。吸收和散射的影响，低规律性系数建模，纳入这些问题的制定。这种时间反演方法导致收敛的迭代过程，以重建的初始条件下，散射系数是足够小的$L^{\infty}$规范。然后，使用对偶参数，我们证明了反问题的可解性导致精确可控性的运输领域的最小范数控制建设性地获得。这两个问题的解决方案可以在诸如光学成像和用于癌症治疗的辐射递送的优化的领域中具有医学应用。

一维几何中瞬态输运反问题的 ANN-MoC 方法

ANN-MoC Method for Inverse Transient Transport Problems in One-Dimensional Geometry

本文提出 ANN-MoC 方法，通过特征线法求解器生成的数据训练人工神经网络，求解一维几何中由边界标量通量估计吸收系数的瞬态输运反问题，实验证明其估计准确且具应用潜力。