臺灣博碩士論文加值系統

本研究採用由黃鍔(Huang N. E.)等人所提出的經驗模態分解`法為基礎所研發出的互補式總體經驗模態分解法做為邊緣偵測並結合雙向濾波器來達到降低雜訊的應用。此演算法繼承了經驗模態分解法的一些優點，如:(1)可處理非線性與非穩態的訊號。(2)經驗模態分解法與傳統的數值分析方法不同，分析前無須知道基底，即可根據原始訊號本身的特性與性質，自動地將原始訊號拆解出數個本質函數及剩餘函數，以供分析結果之用。而互補式經驗模態分解法也改良了經驗模態分解法的缺點，如(1)在處理經驗模態分解法中，可能因為間歇性的訊號、雜訊及原始訊號邊緣處理上產生問題，故互補式總體經驗模態分解法則加入白噪訊號以便降低其干擾。(2)由於加入了白噪可能會影響到原始訊號的分析結果，故互補式總體經驗分解法則利用了較多次數的加總及互補式的概念使其白噪的影響降到最低，使其分析的結果趨近於正解。
互補式總體經驗模態分解法可將影像圖形訊號分解成數個無模態混雜、線性且穩定的本質模態函數，運算後的波形訊號須符合本質模態函數的條件。而本質模態函數則可以了解一些影像訊息，其剩餘函數則凝聚了原始影像圖形中的光影的特性。
目前一維經驗模態分解法已有大量的文獻證明其有調適性及可運用在非線性非穩態訊號的能力。本研究採用的二維總體經驗模態分解法，其應用在影像處理上可從原始影像訊號取得一些訊息，如: 原始影像訊號中局部特徵區域、邊緣結構及光影明暗變化。最後把得到的影像結合雙向濾波器做處理，提出一種新的濾波器以改善雜訊問題。由我的們研究結果顯示，互補式經驗模態分解法確實可偵測影像中的邊緣，並且可得到較為清晰的邊緣影像。並結合雙向濾波器來降低訊，取得更為清晰的影像。

In this study, by Huang NE, who proposed the complementary empirical mode decomposition method based on the empirical mode decomposition method. The algorithm inherits the empirical mode decomposition some of the benefits. For example it can solve nonlinear and nonstationary signals. Another Empirical mode decomposition method and the traditional numerical methods, the base need to know prior to analysis, the original signals can be based on the characteristics and nature of the original signal automatically a number of nature apart from the function and the remaining functions for analysis. Complementary empirical mode decomposition method also improved the empirical mode decomposition shortcomings. For example the intermittent signals, noise and the edge of the original signal processing have problems in Empirical mode decomposition method, so Complementary empirical mode decomposition method can solve problems by white noise. Another joining the white noise may affect the analysis of the original signal, so the Complementary empirical mode decomposition method are more general and increase the number of complementary concepts to minimize the impact of white noise, the results of analysis tends to positive solutions.
Complementary empirical mode decomposition method can decompose the image into several graphic signals without mode mixing, linear and stable intrinsic mode functions, computing the signal waveform after the intrinsic mode functions to comply with the conditions. Intrinsic mode functions to establish original signal can understand some of original signal information, the remaining factor is the combination of the characteristics of the original image graph.
One-dimensional empirical mode decomposition method have a lot of literature to proof of adaptability and it can be used in the ability of nonlinear and nonstationary signals. In this study, the two-dimensional empirical mode decomposition method, the application in image process can be obtained from the original number of information. Local feature in the original image signal area, the edge structure and light shading. Finally, to get the information to do with Bilateral Filter processing, a new method to improve noise issues.

中文摘要 I
Abstract III
目錄 1
表目錄 2
圖目綠 3
第一章 緒論 5
1.1 前言 5
1.2 前人研究 6
1.3 研究目的與動機 7
1.4 論文架構 8
第二章　文獻探討 9
2.1 小波分析(Wavelet analysis) 9
2.2 二代小波分析(Second Generation Wavelet Transform) 12
2.3 雙向濾波器(Bilateral filter) 14
2.4 峰值信噪比 (Peak signal to noise ratio) 15
2.5 結構相似度 (Structural Similarity Index) 15
第三章 實驗材料與方法 17
3.1 經驗模態分解法(Empirical Mode Decomposition, EMD) 17
3.2 總體式經驗模態分解法( Ensemble EMD) 27
3.3 多維總體經驗模態分解法 (Multi-Dimension EEMD) 32
3.4 互補式總體經驗模態分解法(Complementary EEMD) 37
第四章　實驗結果與分析 40
4.1 T2-weighted MRI Brain Image 40
4.2 T2-weighted MRI prostate Image 43
4.3 Lena+9% Gaussian 46
4.4 T1-weighted MRI Brain Image + 9% Rayleigh Noise 51
第五章　結論與未來展望 56
References 58

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