多維濾波器應用於腦電位分佈

Abstract

本論文的主要研究目的是發展一三維(3D)濾波器，並將其運用於腦殼表面電位分佈的處理上。基本上，腦電位分佈的處理為有限的錄製電極（空間解析度）所侷限，因此，針對此一瓶頸，我們提出了一可行的解決途徑，稱之為「三維濾波法」(the 3D filtering method)，此提出的解決方法不僅已被發展用來推測腦電位的空間分佈，經過我們對以往已提出的方法（包括廣被利用的「四點最近法」(the 4NN method)和「電耦極模式法」(the current dipole model)做一番比較後發現，這樣的解決方式確實能提供另一個具潛力的途徑來推測整個腦電位分佈。而在本論文中，不論是在時域或頻域，我們也會論及一些多維濾波器設計的基本原理和法則，特別是三維濾波器的設計及研究。 本論文中，根據三個不同方法所設計的三維濾波器被應用於重建電位的空間分佈，由此，我們再分析三維濾波器的特性（如頻寬）對腦電位分佈的影響。除此之外，為了更進一步的瞭解傳統解決方式及此一方法的優缺點，我們亦在第四章作一番比較。最後我們再利用「三維濾波法」來進行一些實驗研究如集中性放電波(EEG focal activity)一致性(homogeneity)的探討等等。我們相信「三維濾波法」不僅能直接、有效地對多頻道腦波訊號作空間上的分析，它本身更兼顧了物理上的意義並且融合了多維濾波器的優點及潛力。

The purpose of this research is to develop three-dimensional (3D) filters on manipulating the distribution of the brain electrical potential on the scalp based on a limited number of EEG recording electrodes (spatial resolution). An alternative called the 3D filtering method is developed to interpolate scalp potential distributions. In comparison with the widely used 4NN method and the current dipole model, the 3D filtering method is demonstrated to have competitive performance. In addition, some primary principles and algorithms to design multidimensional filters, especially threedimensional FIR filters, are mentiaoned in detail both in frequency and spatial domain in this thesis. The 3D filters, designed according to 3 different methods, are then applied to reconstruction of brain potential mapping. We then investigate the effects of the 3D filters' characteristics (e.g., bandwidth of the filter) on constructed brain mapping. To further understand the advantages and drawbacks of conventional methods and our method, we devote Chapter 4 to the comparison. Finally, we applied the 3D filtering method proposed in this thesis to an interesting case study, i.e., exploration of the homogeneity property of EEG focal activity. To our belief, this approach, which explores the forte and potentiality of multidimensional filters, provides a straightforward, physically meaningful, and efficient approach to deal with multi-channel EEG signals.