IEEE Trans Med Imaging. 2018 Sep;37(9):1957-1969. doi: 10.1109/TMI.2017.2739740. Epub 2017 Aug 14.
Coherence and causality measures are often used to analyze the influence of one region on another during analysis of functional brain networks. The analysis methods usually involve a regression problem, where the signal of interest is decomposed into a mixture of regressor and a residual signal. In this paper, we revisit this basic problem and present solutions that provide the minimal-entropy residuals for different types of regression filters, such as causal, instantaneously causal, and noncausal filters. Using optimal prediction theory, we derive several novel frequency-domain expressions for partial coherence, causality, and conditional causality analysis. In particular, our solution provides a more accurate estimation of the frequency-domain causality compared with the classical Geweke causality measure. Using synthetic examples and in vivo resting-state functional magnetic resonance imaging data from the human connectome project, we show that the proposed solution is more accurate at revealing frequency-domain linear dependence among high-dimensional signals.
相干性和因果性度量常被用于分析功能脑网络中一个区域对另一个区域的影响。分析方法通常涉及回归问题，其中感兴趣的信号被分解为回归器和残差信号的混合物。在本文中，我们重新研究了这个基本问题，并提出了针对不同类型回归滤波器（如因果滤波器、即时因果滤波器和非因果滤波器）的最小熵残差的解决方案。我们使用最优预测理论，为部分相干性、因果性和条件因果性分析推导出了几个新的频域表达式。特别是，与经典的 Geweke 因果度量相比，我们的解决方案提供了对频域因果关系更准确的估计。使用合成示例和来自人类连接组计划的体内静息态功能磁共振成像数据，我们表明，所提出的解决方案在揭示高维信号之间的频域线性依赖关系方面更加准确。
