This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological tissue, but the high computational cost associated with its solution has hindered its use in time-domain optical-tomography and other areas. In this paper this problem is tackled by means of a number of computational and modeling innovations, including (1) A spatial parallel-decomposition strategy with perfect parallel scaling for the forward and inverse problems of optical tomography on parallel computer systems; and, (2) A Multiple Staggered Source method (MSS) that solves the inverse transport problem at a computational cost that is independent of the number of sources employed, and which significantly accelerates the reconstruction of the optical parameters: a six-fold MSS acceleration factor is demonstrated in this paper. Finally, this contribution presents (3) An intuitive derivation of the adjoint-based formulation for evaluation of functional gradients, including the highly-relevant general Fresnel boundary conditions—thus, in particular, generalizing results previously available for vacuum boundary conditions. Solutions of large and realistic 2D inverse problems are presented in this paper, which were produced on a 256-core computer system. The combined parallel/MSS acceleration approach reduced the required computing times by several orders of magnitude, from months to a few hours.

本文提出了一种用于时域光学层析成像的有效的基于并行辐射传输的反问题求解器。辐射传输方程为光子在生物组织中的传输提供了物理上精确的模型，但与其解决方案相关的高计算成本阻碍了其在时域光学断层扫描和其他领域的应用。在本文中，这个问题通过许多计算和建模创新来解决，包括（1）一种空间并行分解策略，具有完美的并行缩放，用于并行计算机系统上的光学断层扫描的正向和逆向问题；(2) 一种多交错源方法 (MSS)，它以计算成本解决逆传输问题与使用的光源数量无关，并且显着加速了光学参数的重建：本文展示了六倍 MSS 加速因子。最后，这一贡献提出了 (3) 用于评估功能梯度的基于伴随的公式的直观推导，包括高度相关的一般菲涅耳边界条件 - 因此，特别是概括了以前可用于真空边界条件的结果。本文介绍了大型且现实的二维逆问题的解决方案，这些解决方案是在 256 核计算机系统上生成的。组合的并行/MSS 加速方法将所需的计算时间减少了几个数量级，从几个月减少到几个小时。