Approximation errors and model reduction with an application in optical diffusion tomography
Approximation errors and model reduction with an application in optical diffusion tomography
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DOI：
10.1088/0266-5611/22/1/010
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发表时间：
2006-02-01
期刊：
影响因子：
2.1
通讯作者：
Vauhkonen, M
中科院分区：
文献类型：
--
作者：
Arridge, SR;Kaipio, JP;Vauhkonen, M
在几个应用中，通常由于可用时间、计算机内存或其他限制，通常需要模型降阶。在与偏微分方程有关的问题中，这通常意味着我们必须在模型中使用稀疏网格来求解正问题。相反，如果我们被给予越来越准确的测量，我们必须使用越来越精确的正向问题解算器来利用测量中的信息。光学扩散层析成像(ODT)是一个例子，其中正问题解算器所需的典型精度导致计算时间在生物医学和工业终端应用中都是不可接受的。本文回顾了近似误差理论，研究了光学扩散层析成像中网格密度和测量精度之间的相互影响。我们证明，如果估计和使用近似误差，则可以使用传统测量模型无法接受的网格密度。
Model reduction is often required in several applications, typically due to limited available time, computer memory or other restrictions. In problems that are related to partial differential equations, this often means that we are bound to use sparse meshes in the model for the forward problem. Conversely, if we are given more and more accurate measurements, we have to employ increasingly accurate forward problem solvers in order to exploit the information in the measurements. Optical diffusion tomography (ODT) is an example in which the typical required accuracy for the forward problem solver leads to computational times that may be unacceptable both in biomedical and industrial end applications. In this paper we review the approximation error theory and investigate the interplay between the mesh density and measurement accuracy in the case of optical diffusion tomography. We show that if the approximation errors are estimated and employed, it is possible to use mesh densities that would be unacceptable with a conventional measurement model.