Estimation of modeling errors and their regularization in applied inverse problems

我们已经获得了一些新的成果作为扩散光学断层扫描（DOT）的基础研究，该技术被认为是一项即将到来的技术。这些结果是对DOT对应的数学模型从数学和计算两个方面进行深入思考而得出的。我们仅限于对传输方程模型中的误差进行建模，该模型被视为光子在生物医学组织中传播的基本数学模型。通过理论论证和计算，我们指出了以往基于反问题数学分析的DOT研究中的一些致命误解。

We have obtained some new results as fundamental study for the diffused optical tomography (DOT), which is considered as a coming technology. The results are deduced through deep consideration, from both mathematics and computing, about mathematical models corresponding to DOT.In the project study, we focus on modeling errors which arise in mathematical modeling; we restrict ourselves to modeling errors in the transport equation model which is regarded as the fundamental mathematical one for propagation of photons in biomedical tissues. Through theoretical arguments and computings, we have pointed out some fatalmisunderstanding in the past studies for DOT based on mathematical analysis of the inverse problems.