In this paper, we revisit the bioluminescence tomography (BLT) problem, where one seeks to reconstruct bioluminescence signals (an internal light source) from external measurements of the Cauchy data. As one kind of optical imaging, the BLT has many merits such as high signal-to-noise ratio, non-destructivity and cost-effectiveness etc., and has potential applications such as cancer diagnosis, drug discovery and development as well as gene therapies and so on. In the literature, BLT is extensively studied based on diffusion approximation (DA) equation, where the distribution of peak sources is to be reconstructed and no solution uniqueness is guaranteed without adequate a priori information. Motivated by the solution uniqueness issue, several theoretical results are explored. The major contributions in this work that are new to the literature are two-fold: first, we show the theoretical uniqueness of the BLT problem where the light sources are in the shape of $C^2$ domains or polyhedral- or corona-shaped; second, we support our results with plenty of problem-orientated numerical experiments.

翻译：本文重新审视了生物发光断层成像（BLT）问题，该问题旨在从外部测量的柯西数据重建生物发光信号（内部光源）。作为一种光学成像技术，BLT具有信噪比高、无损检测、成本效益好等优点，在癌症诊断、药物发现与开发以及基因治疗等领域具有潜在应用价值。现有文献中，BLT研究主要基于扩散近似（DA）方程，通过重建峰值光源分布实现成像，但在缺乏充分先验信息时无法保证解的唯一性。针对解的唯一性问题，本文探索了若干理论结果。本文的主要创新贡献包括两方面：首先，证明了当光源具有$C^2$域、多面体形或冠形结构时BLT问题的理论唯一性；其次，通过大量面向问题的数值实验验证了理论结果。