Kiebel S J, Poline J B, Friston K J, Holmes A P, Worsley K J
Department of Neurology, Friedrich-Schiller-University, Jena, Germany.
Neuroimage. 1999 Dec;10(6):756-66. doi: 10.1006/nimg.1999.0508.
The assessment of significant activations in functional imaging using voxel-based methods often relies on results derived from the theory of Gaussian random fields. These results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated. End results (i. e., P values associated with local maxima, clusters, or sets of clusters) critically depend on this assessment, which should be as exact and as reliable as possible. In some earlier implementations of statistical parametric mapping (SPM) (SPM94, SPM95) the smoothness was assessed on Gaussianized t-fields (Gt-f) that are not generally free of physiological signal. This technique has two limitations. First, the estimation is not stable (the variance of the estimator being far from negligible) and, second, physiological signal in the Gt-f will bias the estimation. In this paper, we describe an estimation method that overcomes these drawbacks. The new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated t-field. Knowing the smoothness of these component fields is important because it allows one to compute corrected P values for statistical fields other than the t-field or the Gt-f (e.g., the F-map) and eschews bias due to deviation from the null hypothesis. We validate the method on simulated data and demonstrate it using data from a functional MRI study.
使用基于体素的方法评估功能成像中的显著激活通常依赖于源自高斯随机场理论的结果。这些结果解决了多重比较问题，并假设数据的空间相关性或平滑性是已知的或可以估计的。最终结果（即与局部最大值、簇或簇集相关的P值）严重依赖于这种评估，而这种评估应该尽可能精确和可靠。在统计参数映射（SPM）的一些早期实现（SPM94、SPM95）中，平滑性是在通常并非完全没有生理信号的高斯化t场（Gt-f）上进行评估的。该技术有两个局限性。第一，估计不稳定（估计器的方差远非可忽略不计），第二，Gt-f中的生理信号会使估计产生偏差。在本文中，我们描述了一种克服这些缺点的估计方法。新方法涉及估计标准化残差场的平滑性，该平滑性近似于相关t场的分量场的平滑性。了解这些分量场的平滑性很重要，因为它允许人们为除t场或Gt-f之外的统计场（例如F映射）计算校正后的P值，并避免由于偏离原假设而产生的偏差。我们在模拟数据上验证了该方法，并使用功能磁共振成像研究的数据进行了演示。
