时域光学层析成像的并行反问题求解器
Parallel inverse-problem solver for time-domain optical tomography with perfect parallel scaling
摘要：
提出了一种基于并行辐射转移的时域光学层析成像反问题求解器。辐射转移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，但是与其解相关的高计算成本阻碍了其在时域光学层析成像和其他领域中的应用。本文通过一系列计算和建模创新来解决这一问题，包括：1）在并行计算机系统上实现光学层析成像正逆问题的空间并行分解策略和完全并行缩放;以及，2）多交错源方法（MSS），其以与所采用的源的数量无关的计算成本来解决逆输运问题，并且显著地加速了光学参数的重建：本文证明了六倍的MSS加速因子。最后，这篇文章提出了3）一个直观的推导伴随为基础的公式，用于评估功能梯度，包括高度相关的一般菲涅耳边界条件-因此，特别是，概括以前可用的真空边界条件的结果。本文给出了在256核计算机系统上求解大型、实际二维反问题的结果。结合并行/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。
英文摘要：
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.
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