Cohen-Bacrie C, Goussard Y, Guardo R
Ecole Polytechnique, Biomedical Engineering Institute, Montreal, P.Q., Canada.
IEEE Trans Med Imaging. 1997 Oct;16(5):562-71. doi: 10.1109/42.640745.
This paper describes a new approach to reconstruction of the conductivity field in electrical impedance tomography. Our goal is to improve the tradeoff between the quality of the images and the numerical complexity of the reconstruction method. In order to reduce the computational load, we adopt a linearized approximation to the forward problem that describes the relationship between the unknown conductivity and the measurements. In this framework, we focus on finding a proper way to cope with the ill-posed nature of the problem, mainly caused by strong attenuation phenomena; this is done by devising regularization techniques well suited to this particular problem. First, we propose a solution which is based on Tikhonov regularization of the problem. Second, we introduce an original regularized reconstruction method in which the regularization matrix is determined by space-uniformization of the variance of the reconstructed condictivities. Both methods are nonsupervised, i.e., all tuning parameters are automatically determined from the measured data. Tests performed on simulated and real data indicate that Tikhonov regularization provides results similar to those obtained with iterative methods, but with a much smaller amount of computations. Regularization using a variance uniformization constraint yields further improvements, particularly in the central region of the unknown object where attenuation is most severe. We anticipate that the variance uniformization approach could be adapted to iterative methods that preserve the nonlinearity of the forward problem. More generally, it appears as a useful tool for solving other severely ill-posed reconstruction problems such as eddy current tomography.
本文描述了一种用于电阻抗断层成像中电导率场重建的新方法。我们的目标是改善图像质量与重建方法数值复杂度之间的权衡。为了减少计算量，我们对描述未知电导率与测量值之间关系的正向问题采用线性化近似。在此框架下，我们专注于找到一种合适的方法来应对主要由强衰减现象导致的问题不适定性；这通过设计适用于此特定问题的正则化技术来实现。首先，我们提出一种基于问题的蒂霍诺夫正则化的解决方案。其次，我们引入一种原始的正则化重建方法，其中正则化矩阵由重建电导率方差的空间均匀化确定。两种方法都是无监督的，即所有调谐参数都根据测量数据自动确定。对模拟数据和实际数据进行的测试表明，蒂霍诺夫正则化提供的结果与迭代方法获得的结果相似，但计算量要小得多。使用方差均匀化约束的正则化进一步改进了结果，特别是在未知物体衰减最严重的中心区域。我们预计方差均匀化方法可适用于保留正向问题非线性的迭代方法。更一般地说，它似乎是解决其他严重不适定重建问题（如涡流断层成像）的有用工具。
