含空洞散射介质中基于输运模型和水平集的形状重建
Shape reconstruction in scattering media with voids using a transport model and level sets
AI总结：
本文提出一种结合输运-反向输运与水平集及伴随场技术的两步形状重建方法，用于扩散光学层析成像中快速高精度地恢复含空洞散射介质内的多个障碍物。
摘要：
本文提出了一种用于扩散光学层析成像（DOT）的两步形状重建方法，该方法利用伴随场和水平集技术。近红外光子在组织中的传播由含时线性输运方程建模，其中吸收参数需根据边界测量数据重建。在形状重建方法中，假设非均匀背景吸收参数和障碍物内部的值（通常与背景具有高对比度）已知，但障碍物的数量、大小、形状和位置需从数据中重建。由于介质中存在所谓的清晰区域，带来了额外的困难。重建方案的第一步是输运-反向输运（TBT）方法，该方法为我们提供了所寻目标的低对比度近似。第二步利用该结果作为求解形状重建问题的初始猜测。此第二步的关键点在于融合用于表示重建障碍物形状的“水平集技术”和用于求解非线性逆问题的“伴随场技术”。数值实验表明，该新方法能够快速且高精度地恢复一个或多个目标。
英文摘要：
A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport equation, of which the absorption parameter has to be reconstructed from boundary measurements. In the shape reconstruction approach, it is assumed that the inhomogeneous background absorption parameter and the values inside the obstacles (which typically have a high contrast to the background) are known, but that the number, sizes, shapes, and locations of these obstacles have to be reconstructed from the data. An additional difficulty arises due to the presence of so-called clear regions in the medium. The first step of the reconstruction scheme is a transport-backtransport (TBT) method which provides us with a low-contrast approximation to the sought objects. The second step uses this result as an initial guess for solving the shape reconstruction problem. A key point in this second step is the fusion of the 'level set technique' for representing the shapes of the reconstructed obstacles, and an 'adjoint-field technique' for solving the nonlinear inverse problem. Numerical experiments are presented which show that this novel method is able to recover one or more objects very fast and with good accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
