基於標準與特別演繹樣本訊號元素之稀疏訊號處理法於腦電圖中觸發電位與獨立成份訊號之分析

Abstract

稀疏信號在選定某個恰當的訊號樣本庫之下，在使用其中的訊號元素拆解後有很大一部分的訊號能量會集中於某幾個少數的元素，此種訊號表達方式可以使用遠低於 Nyquist 訊號取樣限制的資料量來表達一個稀疏訊號，或擷取出其中占大部分能量的訊號成分。稀疏信號處理是應用數學與稀疏表達法的交集結果。也是未來實現遠距醫療與病患檢測上的一項重要技術，將會大大地降低儲存訊號所使用的資料量。 探討如何選用一個能僅用少量元素即可拆解一訊號大部分能量的訊號樣本庫在稀疏訊號處理上是非常重要的。在可使用時間、頻率、規模參數來控制樣本庫中訊號的波形的完備Gabor樣本庫已知為一種能有效率地拆解腦電圖儀（EEG）的訊號樣本庫。 本文將著重介紹一個基於Matching Pursuit ，並配合改進後的 Grassmannian參數取樣方式以及自然梯度設計而出的文化基因演算法。

A sparse signal has a large portion of its energy contained in a small number of coefficients, which can be represented with number of samples significantly beneath the Nyquist’s criterion. Sparse signal processing is the application of the mathematics of sparse representations in signal processing. This is essential for ubiquitous medicine and healthcare due to the immense amount of data required for each individual patient monitoring. A representation dictionary for the target signal space with only minimal number of supports is critical to the stability and consistency of the sparse signal processing schema when employing pursuit algorithms. The overcomplete Gabor dictionary, which can be parameterized into time, frequency, scale and phase, is already known to have efficient representation for electroencephalograms (EEGs). This thesis includes a Memetic Algorithm based on Matching Pursuit for EEG signal decompositions, and an improved parameter sampling and optimization method for the Gabor dictionary based on natural gradient and Grassmannian concepts.