Jiang Ming, Zhou Tie, Cheng Jiantao, Cong Wenxiang, Wang Ge
Opt Express. 2007 Sep 3;15(18):11095-116. doi: 10.1364/oe.15.011095.
The bioluminescence tomography is a novel molecular imaging technology for small animal studies. Known reconstruction methods require the completely measured data on the external surface, although only partially measured data is available in practice. In this work, we formulate a mathematical model for BLT from partial data and generalize our previous results on the solution uniqueness to the partial data case. Then we extend two of our reconstruction methods for BLT to this case. The first method is a variant of the well-known EM algorithm. The second one is based on the Landweber scheme. Both methods allow the incorporation of knowledge-based constraints. Two practical constraints, the source non-negativity and support constraints, are introduced to regularize the BLT problem and produce stability. The initial choice of both methods and its influence on the regularization and stability are also discussed. The proposed algorithms are evaluated and validated with intensive numerical simulation and a physical phantom experiment. Quantitative results including the location and source power accuracy are reported. Various algorithmic issues are investigated, especially how to avoid the inverse crime in numerical simulations.
生物发光断层扫描是一种用于小动物研究的新型分子成像技术。已知的重建方法需要外表面的完整测量数据，而实际上只能获得部分测量数据。在这项工作中，我们从部分数据出发为生物发光断层扫描建立了一个数学模型，并将我们之前关于解的唯一性的结果推广到部分数据情况。然后，我们将两种生物发光断层扫描的重建方法扩展到这种情况。第一种方法是著名的期望最大化（EM）算法的一个变体。第二种方法基于兰德韦伯（Landweber）格式。这两种方法都允许纳入基于知识的约束。引入了两个实际约束，即源非负性和支持约束，以正则化生物发光断层扫描问题并产生稳定性。还讨论了这两种方法的初始选择及其对正则化和稳定性的影响。通过密集的数值模拟和物理体模实验对所提出的算法进行了评估和验证。报告了包括位置和源功率精度在内的定量结果。研究了各种算法问题，特别是如何在数值模拟中避免反问题犯罪。
