Higher Order Statistics-based Radial Basis Function Network for Evoked Potentials

誘發電位是腦經由外界刺激，如聲音，光線，電刺激等所產反應。它們可以提供在神經徑路病變和其他神經系統診斷相關的重要資訊。然而誘發電位通常隱藏在自發性的背景腦電活動中，而且它的訊雜比非常低。如何有效地取出誘發電位仍是一項有困難性的工作。一般在臨床上總體平均法是最常被使用來取出誘發電位的方式。然而使用平均法需要大量的重複刺激來取得誘發電位，而且可能遺失掉刺激過程中每筆誘發電位間的變動差異資訊。近年來，有許多如何有效減少刺激次數來取出誘發電位的相關研究被進行探討。可適性濾波技術是其中一個被廣泛發展在誘發電位應用上的技術。在本論文中，各種可適性濾波技術在誘發電位應用上的架構將被清楚地介紹以及討論。此外，本論文並提出使用高階統計徑向基函數神經網路來取出誘發電位。藉由高階統計可以提供對稱性分布隨機信號的抑制特性，高階統計學習演算法被使用來降低雜訊對於可適性濾波效能上的影響。從模擬和實驗的結果得知，使用高階統計學習演算法的效能除了對於學習速率的選擇較不敏感外，在不同的訊雜比環境下，使用高階統計學習演算法的效果均如預期中較使用最小均方演算法所得到的效果佳。因此，高階統計徑向基函數神經網路可以做為在誘發電位應用上的有效方式。Evoked potentials are responses of the brain to external stimuli, such as sounds, lights and electrical stimuli. They can provide useful information in the diagnosis of nerve systems. However, evoked potentials are typically embedded in the ongoing electroencephalogram with a very poor signal-to-noise ratio. Thus, how to effectively extract evoked potentials is a difficult task. Traditionally, ensemble averaging method is most frequently used for evoked potentials. However, it requires a great number of stimuli to obtain evoked potentials. And it may lose information of trial-to-trial variation. Recently, a number of methods have been investigated for evoked potentials with a minimum of required stimuli repetitions. Adaptive filtering is one of techniques widely developed for evoked potentials. In this thesis, different kinds of schemes of adaptive filtering for evoked potentials were introduced and discussed in detail. Single-trial estimation for evoked potentials by using higher order statistics-based radial basis function network was also proposed. Higher order statistics provides a natural tolerance to symmetrically distributed stochastic signals. By using higher order statistics-based learning algorithm can effectively reduce the influence of additive noises on learning. From simulations and experiments, as our expectation, the performance by using higher order statistics-based learning algorithm is insensitive to the selection of learning rate, and is superior to that by using least mean square algorithm under different noise levels. Thus, higher order statistics-based radial basis function network may be served as a useful tool for evoked potentials.ABSTRACT i LIST OF FIGURES v LIST OF TABLES vii CHAPTER 1 INTRODUCTION 1 1.1 Motivation 1 1.2 Objective 10 1.3 Dissertation organization 11 CHAPTER 2 BACKGROUND 13 2.1 Electrical activity of the brain 14 2.2 Evoked potentials 19 2.2.1 Visual evoked potentials 19 2.2.2 Auditory evoked potentials 22 2.2.3 Somatosensory evoked potentials 24 CHAPTER 3 METHODOLOGY 27 3.1 Higher order statistics of stochastic signals 29 3.1.1 The definition and properties of higher order statistics 29 3.1.2 Relationship between moments and cumulants 34 3.1.3 Higher order statistics for stationary process 35 3.2 Associative memory networks 37 3.2.1 Functional link network 39 3.2.2 Radial basis function network 40 3.3 Supervised learning algorithm 43 3.3.1 Least mean square algorithm 43 3.3.2 Higher order statistics-based learning algorithm 46 3.4 Single-trial estimation for evoked potentials 52 CHAPTER 4 RESULTS AND DISCUSSION 55 4.1 Simulations for extracting evoked potentials 55 4.2 Experiments for extracting evoked potentials 68 4.2.1 Human visual evoked potentials 68 4.2.2 Intra-operative somatosensory evoked potentials 76 CHAPTER 5 CONCLUSION 85 REFERENCE 8