禪坐和休息腦電波的小波變異性之主成分分析

Abstract

本論文以小波係數變異數的估算和針對變異數矩陣的主成分分析，試圖探討腦電波中各個部位的高頻成分。腦電波訊號分別從兩組的自願者錄製。實驗組與控制組分別是八位有禪作經驗的修行者和八位健康的受測者。首先我們先將總長兩分鐘的腦電波分段，每段長一秒，在同一段時間區間裡，使用最大重複離散小波轉換（Maximal Overlap Discrete Wavelet Transform）來求出30個電極的腦電波的小波係數，之後再個別估算小波係數的變異數。對於每個電極，可以從七段對應於不同的腦電波頻段的區間求出七個變異數。於是每段一秒的腦電波可以用這七組變異數組成的特徵向量來表示。利用這七組變異數去代表原本的一秒長度訊號，我們會建構出三十乘以七的矩陣，針對這個矩陣去執行主成分分析求出每個電極訊號針對第一個主成分的映射值。利用不同的變異數以及第一主成分的大腦映射可以提供我們辨認腦電波不同頻段的空間聚焦性。 在這篇論文中，會將預分析的腦波訊號，以每段一秒執行上述分析，之後再針對每一個電極，將取完絕對值的第一主成分映射值作平均並比較。 實驗/控制組受測者被要求在心智壓力測試以及禪坐/休息的實驗流程。本論文中，根據鄰近的電極將人的腦區分為前腦（Frontal）、後腦（Posterior）、右腦（Right temporal）、左腦（Left temporal）、中腦（Central）。我們主要會針對前心算雨後心算的腦波作分析比較。研究結果發現，對於控制組受測者，中間經過一段長時間的放鬆休息，對於腦中高頻成分的變化並沒有顯著的影響。對實驗組而言，做完禪坐之後，腦中的高頻成分的變化會比控制組還要明顯。

This thesis is aimed to investigate the high-frequency components in EEG signals by estimating the variance of wavelet coefficients and analyzing the principle components of variance matrix. EEG’s were recorded from two groups of volunteers. Experimental and control group involved respectively eight experienced Chan-Meditation practitioners and eight healthy control subjects within the same age range. First we decomposed the 2-minute EEG signals into one-second epochs. For each epoch, Maximal Overlap Discrete Wavelet Transform（MODWT）was employed to evaluate the wavelet coefficients and then estimate the variance of wavelet coefficients for all 30 channels. For each channel, seven variances were computed for seven wavelet scales corresponding to different EEG rhythms. Accordingly, each one-second epoch can be represented by a feature vector composed of 7 variances. Then, for the 30-channel EEGs, we constructed a 30-by-7 matrix and applied PCA (Principle Component Analysis) to obtain the mapping of the first principle component（PC1）. Brain mappings of different variances and PC1 allow us to identify the spatial focalization of particular EEG rhythms. In this study, we analyzed one-second epochs of EEG. After analyzing the whole signal, average mapping of PC1 was compared. Brain spatio-spectral characteristics of experimental/control volunteers under mental stress and meditation/rest were explored by dividing the brain cortex into five regions of local neural networks, frontal (F), parietal (P), right-temporal (R), left-temporal (L) and central (C) regions, defined by five clusters of nearby EEG channels. We focused on analyzing EEG of pre-mental-stress-test session and post-mental-stress-test session and compared the results. For control group, difference of the high-frequency components between these two sessions is not significant. For experimental group, after Chan-meditation practice, variation of the high-frequency components is more significant than control group.