# 臺灣博碩士論文加值系統

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 獨立成份分析（Independent Component Analysis, 簡稱ICA）是從1990開始發展的資訊處理技術，其主要目的是從觀察到的混合資料（Mixing data）中找出原始資料（Sources）。 ICA可依據混合矩陣A（Mxm）分成完備獨立成份分析（M=m）與過度完備獨立成份分析（M>m），而ICA實際應用大多是過度完備的情況，其混合矩陣為長方形矩陣，必須從低維度的混合資料找回原本高維度的原始資料，所以過度完備的ICA問題比完備的ICA還複雜許多。 本論文針對Chen（2003）所提出的NullICA方法,在原始資料為雙倍指數（Double Exponential, 簡稱DE）分配假設下，利用模擬資料及聲音資料於過度完備的ICA情況下分析NullICA的特性、效能與限制，最後成功將NullICA演算法應用在影像特徵擷取的影像處理上。
 Independent component analysis (also called ICA) is an algorithm developed since 1990. The goal of ICA is to estimate the unknown mixing matrix A and to recover the original sources s given only the observations x in which x=As. According to the structure of the Mxm mixing matrix A, ICA can divided into complete ICA (M=m) and overcomplete ICA (M>m). In most ICA applications, the overcomplete situations are usually seen in which the mixing matrix A is a rectangular matrix with more columns than rows. It means that we must recover high dimensional sources from low dimensional observation data. In this way, the overcomplete ICA question is more complicated.In this thesis, the NullICA algorithm (Chen 2003) was employed based on the assumption that the sources are distributed in a Double Exponential fashion. To analyze the characteristics, efficiency and the constraints of NullICA algorithm on the overcomplete ICA situation, both the simulated and real sound data are tested. Finally we successfully applied the NullICA algorithm on extracting basis features from image frames.
 目錄1：緒論 41.1研究背景介紹..........................................41.2文獻回顧..............................................92：NullICA演算法 122.1零核空間在過度完備線性系統下的表現形式....................122.2NullICA參數估計架構....................................132.3Langevin-EulerMoves演算法.............................152.4TheGivensSampler演算法................................163：NullICA演算法在原始資料為DE分配的情況下 193.1估計參數c.............................................193.2估計參數D.............................................203.3估計參數U與V...........................................233.4DE分配參數α的估計與分析.................................244：實驗結果 274.1模擬..................................................274.2盲蔽訊號源分離..........................................374.3NullICA演算法的特性、效能與限制..........................414.3.1觀察-假設混合矩陣A已知.................................414.3.2觀察-假設c固定已知....................................444.3.3觀察-假設參數D已知....................................494.4影像特徵擷取............................................505：研究成果及討論 57附錄 58參考文獻 68
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