Abstract Optical tomography is a typical non-invasive medical imaging technique, aiming to reconstruct the optical properties of tissues from boundary measurements by passing near infrared light through the tissues. We are concerned with the forward and inverse problems for a time-dependent diffusion equation model arising in diffuse optical tomography. To solve the forward problem, we develop a boundary integral equation method, and then derive a discretization scheme for the resulting system of boundary integral equations. As for the inverse problem, rather than the precise values of the optical parameters, we recover geometric information on unknown inclusions as anomalies where the optical properties are significantly different from the background medium. A noniterative reconstruction method with its rigorous justification is established. Finally, we present some numerical results that illustrate the efficiency and effectiveness of the proposed methods for both the forward and inverse problems.

中文翻译：

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漫射光学层析成像正反问题的数值解

摘要 光学断层扫描是一种典型的非侵入性医学成像技术，旨在通过使近红外光穿过组织，从边界测量重建组织的光学特性。我们关注漫射光学断层扫描中出现的时间相关的扩散方程模型的正向和逆向问题。为了解决前向问题，我们开发了一种边界积分方程方法，然后推导出所得边界积分方程系统的离散化方案。至于逆问题，我们不是通过光学参数的精确值，而是将未知夹杂物的几何信息恢复为异常，其中光学特性与背景介质有显着差异。建立了具有严格论证的非迭代重建方法。