Department of Physics and Mathematics, University of Eastern Finland, FIN-70211 Kuopio, Finland.
IEEE Trans Med Imaging. 2011 Feb;30(2):231-42. doi: 10.1109/TMI.2010.2073716. Epub 2010 Sep 13.
Electrical impedance tomography is a highly unstable problem with respect to measurement and modeling errors. This instability is especially severe when absolute imaging is considered. With clinical measurements, accurate knowledge about the body shape is usually not available, and therefore an approximate model domain has to be used in the computational model. It has earlier been shown that large reconstruction artefacts result if the geometry of the model domain is incorrect. In this paper, we adapt the so-called approximation error approach to compensate for the modeling errors caused by inaccurately known body shape. This approach has previously been shown to be applicable to a variety of modeling errors, such as coarse discretization in the numerical approximation of the forward model and domain truncation. We evaluate the approach with a simulated example of thorax imaging, and also with experimental data from a laboratory setting, with absolute imaging considered in both cases. We show that the related modeling errors can be efficiently compensated for by the approximation error approach. We also show that recovery from simultaneous discretization related errors is feasible, allowing the use of computationally efficient reduced order models.
电阻抗断层成像在测量和建模误差方面是一个高度不稳定的问题。当考虑绝对成像时，这种不稳定性尤其严重。在临床测量中，通常无法准确了解身体形状，因此必须在计算模型中使用近似模型域。先前已经表明，如果模型域的几何形状不正确，则会导致较大的重建伪影。在本文中，我们采用了所谓的逼近误差方法来补偿因身体形状不准确而导致的建模误差。该方法之前已被证明适用于各种建模误差，例如正向模型数值逼近中的粗离散化和域截断。我们使用胸部成像的模拟示例和实验室设置的实验数据来评估该方法，在这两种情况下都考虑了绝对成像。我们表明，逼近误差方法可以有效地补偿相关的建模误差。我们还表明，从同时的离散化相关误差中恢复是可行的，允许使用计算效率高的降阶模型。
