Radich B M, Buckley K M
Department of Electrical Engineering, University of Minnesota, Minneapolis, 55455.
IEEE Trans Biomed Eng. 1995 Mar;42(3):233-41. doi: 10.1109/10.364509.
The Cramer-Rao bound for unbiased dipole location estimation is derived under the assumption of a general head model parameterized by deterministic and stochastic parameters. The expression thus characterizes fundamental limits on EEG dipole localization performance due to the effects of both model uncertainty and statistical measurements noise. Expressions are derived for the cases of multivariate Gaussian and gamma distribution priors, and examples are given to illustrate the derived bounds when the radii and conductivities of a four-concentric sphere head model are allowed to be random. The joint MAP estimate of location/model parameters is then examined as a means of achieving robustness to deviations from an ideal head model. Random variations in both the multiple sphere radii and the layer conductivities are shown, via the stochastic Cramer-Rao bounds and Monte Carlo simulation of the MAP estimator, to have the most impact on localization performance in high SNR regions, where finite sample effects are not the limiting factors. This corresponds most often to spatial regions that are close to the scalp electrodes.
在由确定性和随机参数参数化的一般头部模型假设下，推导了用于无偏偶极子位置估计的克拉美-罗界。因此，该表达式表征了由于模型不确定性和统计测量噪声的影响，脑电图偶极子定位性能的基本限制。推导了多元高斯和伽马分布先验情况下的表达式，并给出了示例，以说明当允许四同心球头部模型的半径和电导率为随机时所推导的界。然后研究位置/模型参数的联合最大后验估计，作为实现对理想头部模型偏差的鲁棒性的一种手段。通过随机克拉美-罗界和最大后验估计器的蒙特卡罗模拟表明，多个球半径和层电导率的随机变化在高信噪比区域对定位性能影响最大，在该区域有限样本效应不是限制因素。这最常对应于靠近头皮电极的空间区域。
