台灣的血液透析 (洗腎) 人口比起其他各國高居世界第一,又台灣健保完全給付
洗腎費用,可見台灣所需支付的洗腎相關醫療費用之龐大。如何提高台灣洗腎病患者
的醫療服務且同時降低醫療器材費用是當務之急。一個有效提高台灣洗腎患者的醫療
服務是 “提供洗腎患者較省錢、省時、省力及有效的血管狹窄量測裝置”,用來量測洗
腎患者是否適合洗腎之血管狀態。台灣工業技術研究院材化所現已開發出專為血管音
訊號量測的強化隨身裝置,本研究將著重於提高該量測裝置的預測準確率 (accuracy)、
敏感度 (sensitivity) 及確度 (specificity) 為發展目標。
本論文提出一系列的科學程序,包括 (1) 使用因子設計有系統地收集量測資料,(2)
使用獨立成份分析 (ICA) 消除血管音中的雜音,及 (3) 提出的創新 ICA 方法論,以幾
何與調和平均不等式為基礎,創立較傳統 ICA 更為有效的獨立成份估測算法。研究結
果已顯示,本論文所提出的創新方法論對於模擬的原始訊號的估計結果差異最小,也就
是,估計的品質較其他獨立成份估測法好。另外,對於血管狹窄的敏感度與確度皆為
100.0 %。對於廔管裝設的敏感度與確度分別為 99.1 % 與 97.9 %,在此部份,其他獨
立成份估測法中表現最好的估測法其敏感度與確度則分別為 96.8 % 與 95.8%。以上的
表現證實,本論文的創新方法論的預測績效皆優於其他獨立成份估測法,且能有效的提
高使用裝置的預測效果。

Taiwan is known to have the greatest number of dialysis patients total com-
pared to other countries. Also, unlike other countries, National Health Insurance
pays 100 percent of the cost of dialysis (i.e., if one has joined National Health In-
surance, one does not need to pay anything at all for dialysis ). Motivated by the
above two facts, the government of Taiwan and researchers have conducted many
studies with the aims of increasing the quality of dialysis service and reducing the
corresponding cost. One recent successful research regarding dialysis comes from
the Industrial Technology Research Institute (ITRI) in Taiwan, which has created
a portable measuring device for vascular sounds (ITRI-PMDV). The device tries
to measure whether a patient’s vascular stenosis is within the safety levels required
before any dialysis treatment.
This research focuses on increasing the sensitivity and specificity of the above-
mentioned ITRI-PMDV, where sensitivity is sometimes called the true positive
rate and the specificity is called the true negative rate. The proposed approach is
based on a series of scientific procedures, including (1) using design of analysis to
collect data systematically, (2) applying independent component analysis (ICA)
to remove the noise of vascular sounds, and (3) solving ICA via a new and more
effective algorithm based on the inequality of the geometric-harmonic means. For
vascular stenoses, results show that the sensitivity and specificity of the proposed
approach all are 100.0 %. For arteriovenous fistulas, results show that the sensi-
tivity and specificity of the proposed approach are 99.1 % and 97.9 % respectively,
while the sensitivity and specificity for the best of the traditional algorithm used
in the current ITRI-PMDV are 96.8 % and 95.8% respectively.

摘要
i
英文摘要
ii
目錄
iii
表目錄
v
圖目錄
vi
第
1
章
緒論
1
1.1
研究背景 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
研究動機與目的 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
研究流程與架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.4
命名定義與數學符號 . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.5
論文架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
第
2
章
文獻探討
12
2.1
訊號處理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2
獨立成份分析
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3
分類與預測 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4
實驗設計與分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
第
3
章
基於幾何與調和平均不等式之創新獨立成份估測法 (GHMI-
ICA)
23
3.1
概念與架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2
統計獨立與平均不等式 . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1
機率密度函數性質與統計獨立定義 . . . . . . . . . . . . . . . . 24
3.2.2
平均不等式定義與性質 . . . . . . . . . . . . . . . . . . . . . . 25
3.2.3
平均不等式與統計獨立結合 . . . . . . . . . . . . . . . . . . . 26
3.3
基於幾何與調和平均不等式的目標函數 . . . . . . . . . . . . . . . . . 26
3.4
創新獨立成份估測演算法 GHMI-ICA 的推導 . . . . . . . . . . . . . . 29
3.5
演算法之績效分析與比較 . . . . . . . . . . . . . . . . . . . . . . . . . 34
第
4
章
廔管裝設與血管狹窄之實證分析
46
4.1
血管音訊號取樣的 24因子實驗設計 . . . . . . . . . . . . . . . . . . . 46
4.2
訊號處理與因子設計分析 . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2.1
訊號處理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2.2
因子設計分析
. . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3
獨立成份估計與因子設計分析 . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1
獨立成份估計
. . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.2
因子設計分析
. . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4
預測績效分析與比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
第
5
章
結論與未來展望
70
參考文獻
73
A
使用的軟體工具
77
B
平均不等式證明
78
C
各獨立成份演算法的分群結果
80
D
GHMI(2) 對於廔管裝設的判別常數與係數
82
E
GHMI(2) 對於血管狹窄的判別常數與係數
85
F
TANH(2) 對於廔管裝設的判別常數與係數
88
G
TANH(2) 對於血管狹窄的判別常數與係數
91

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