Graham B M, Adler A
School of Information Technology and Engineering, University of Ottawa, Canada.
Physiol Meas. 2006 May;27(5):S65-79. doi: 10.1088/0967-3334/27/5/S06. Epub 2006 Apr 18.
An algorithm for objectively calculating the hyperparameter for linearized one-step electrical impedance tomography (EIT) image reconstruction algorithms is proposed and compared to existing strategies. EIT is an ill-conditioned problem in which regularization is used to calculate a stable and accurate solution by incorporating some form of prior knowledge into the solution. A hyperparameter is used to control the trade-off between conformance to data and conformance to the prior. A remaining challenge is to develop and validate methods of objectively selecting the hyperparameter. In this paper, we evaluate and compare five different strategies for hyperparameter selection. We propose a calibration-based method of objective hyperparameter selection, called BestRes, that leads to repeatable and stable image reconstructions that are indistinguishable from heuristic selections. Results indicate: (1) heuristic selections of hyperparameter are inconsistent among experts, (2) generalized cross-validation approaches produce under-regularized solutions, (3) L-curve approaches are unreliable for EIT and (4) BestRes produces good solutions comparable to expert selections. Additionally, we show that it is possible to reliably detect an inverse crime based on analysis of these parameters.
提出了一种用于客观计算线性化单步电阻抗断层成像（EIT）图像重建算法超参数的算法，并将其与现有策略进行比较。EIT是一个病态问题，其中通过将某种形式的先验知识纳入解中来使用正则化计算稳定且准确的解。超参数用于控制数据一致性和先验一致性之间的权衡。一个尚存的挑战是开发和验证客观选择超参数的方法。在本文中，我们评估并比较了五种不同的超参数选择策略。我们提出了一种基于校准的客观超参数选择方法，称为BestRes，它能实现可重复且稳定的图像重建，与启发式选择难以区分。结果表明：（1）超参数的启发式选择在专家之间不一致，（2）广义交叉验证方法产生欠正则化解，（3）L曲线方法对EIT不可靠，（4）BestRes产生的良好解与专家选择相当。此外，我们表明基于这些参数的分析可以可靠地检测逆问题。
