Naruse Yasushi, Takiyama Ken, Okada Masato, Murata Tsutomu
Kobe Advanced ICT Research Center, National Institute of Information and Communications Technology, Kobe, Hyogo 651-2492, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jul;82(1 Pt 1):011912. doi: 10.1103/PhysRevE.82.011912. Epub 2010 Jul 19.
Alpha rhythm is a major component of spontaneous electroencephalographic (EEG) data. We develop a novel method that can be used to estimate the instantaneous phases and amplitudes of the alpha rhythm with high accuracy by modeling the alpha rhythm phase and amplitude as Markov random field (MRF) models. By using a belief propagation technique, we construct an exact-inference algorithm that can be used to estimate instantaneous phases and amplitudes and calculate the marginal likelihood. Maximizing the marginal likelihood enables us to estimate the hyperparameters on the basis of type-II maximum likelihood estimation. We prove that the instantaneous phase and amplitude estimation by our method is consistent with that by the Hilbert transform, which has been commonly used to estimate instantaneous phases and amplitudes, of a signal filtered from observed data in the limited case that the observed data consist of only one frequency signal whose amplitude is constant and a Gaussian noise. Comparison of the performances of observation noise reduction by our method and by a Gaussian MRF model of alpha rhythm signal indicates that our method reduces observation noise more efficiently. Moreover, the instantaneous phase and amplitude estimates obtained using our method are more accurate than those obtained by the Hilbert transform. Application of our method to experimental EEG data also demonstrates that the relationship between the alpha rhythm phase and the reaction time emerges more clearly by using our method than the Hilbert transform. This indicates our method's practical usefulness. Therefore, applying our method to experimental EEG data will enable us to estimate the instantaneous phases and amplitudes of the alpha rhythm more precisely.
阿尔法节律是自发脑电图（EEG）数据的主要组成部分。我们开发了一种新方法，通过将阿尔法节律的相位和幅度建模为马尔可夫随机场（MRF）模型，可用于高精度估计阿尔法节律的瞬时相位和幅度。通过使用置信传播技术，我们构建了一种精确推理算法，可用于估计瞬时相位和幅度并计算边际似然。最大化边际似然使我们能够基于II型最大似然估计来估计超参数。我们证明，在观测数据仅由一个幅度恒定的频率信号和高斯噪声组成的有限情况下，我们方法对瞬时相位和幅度的估计与从观测数据中滤波后的信号通过常用的希尔伯特变换进行瞬时相位和幅度估计的结果一致。我们的方法与阿尔法节律信号的高斯MRF模型在观测噪声降低性能方面的比较表明，我们的方法能更有效地降低观测噪声。此外，使用我们的方法获得的瞬时相位和幅度估计比通过希尔伯特变换获得的更准确。将我们的方法应用于实验EEG数据也表明，与希尔伯特变换相比，使用我们的方法能更清晰地呈现阿尔法节律相位与反应时间之间的关系。这表明了我们方法的实际实用性。因此，将我们的方法应用于实验EEG数据将使我们能够更精确地估计阿尔法节律的瞬时相位和幅度。
