臺灣博碩士論文加值系統

摘要
在這篇論文裡我們陳述關於電阻斷層掃瞄 (EIT) 的一些應用。這個問題牽涉到一個非線性的反問題。關於這個邊界值問題解的唯一性及穩定性已有了一些結果。因為這個反問題是非線性且不適定 (ill-posed) 的，而且測量值並非完全準確，因此並無法精確地找到這個邊界值問題的解。理論上我們可以在某些條件限制下導出電導係數的公式，實際上我們則經由一些數值上的演算法來找電導係數的近似值。
在第二章裡我們列舉出幾個關於這個問題的演算法。這些逼近法分別由一些不同的計算方法所得。首先提到的方法是將原始問題線性化來求得電導係數的近似值。此種演算法是建立在電導係數近似於某個常數的假設之下。另外我們也舉出以遞迴方式來求得電導係數的演算法，例如Wexler 演算法。此外我們也描述其他幾個逼近法，例如 layer-stripping 和 modified Newton-Raphson 演算法。

Table of Contents
Symbols…………………………………………………………………1
Chapter 1 Introduction…………………………………….…….…2
1.1 Physical Background ……..…………………………………...2
1.2 Inverse Problem….……………………………………………2
1.3 Injectivity of ………………………………………………4
1.4 Stability..….………………………………………………….7
1.5 Theoretical Reconstruction .…………………………………….7
Chapter 2 Reconstruction Algorithms ...…………………………13
2.1 Calderon's Approach .…..……………………………………13
2.2 Backprojection Algorithm …………...……….……… ………17
2.3 Wexler Algorithm ….………………………………………..25
2.4 Layer Stripping………………………………………………29
2.5 Some Other Algorithms …...…………………………………33
Chapter 3 Conclusions …..………………………………………..39
Bibliography………………………………………………………..42

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