摘要

一般影像在傳輸過程中，資訊會有所受到影響，使影像的品質受到干擾，其中較常見為脈衝雜訊(Impulsive noise)。在文獻探討方面，針對雜訊的去除主要採用線性或非線性濾波器，其中非線性濾波器的效果明顯比較好，因此本文中，採用了非線性濾波器裡的中值濾波器，結合模糊法則提出了一個新的開關型順序統計的濾波器。
在實現模糊系統時，它的困難度在於如何找出模糊特徵，本研究使用了順序統計跟滑動視窗的誤差值和拉普拉斯邊緣偵測 (Laplacian edge detection)產生模糊特徵值。另外在解模糊化參數的估測方面，本研究分別使用限制型最小平方誤差法(constrained LMS optimization)和基因演算法(genie algorithm)兩種方法來作最佳參數估測並評估其他的效能。
在實驗設計中，分別使用10% 、15% 、20%...等不同比率雜訊、低振幅以及含有高斯雜訊(Gaussion noise)的混合雜訊(Mix noise)來測試本方法的效能。實驗結果顯示，我們的方法比標準型中值濾波器表現大約好1db~2db之間，其中雜訊越大則改善越多。另外在參數的估測使用了限制型平方誤差法與基因演算法，個別改善比沒估測前約0.4~0.6db，ㄧ般而言基因演算法比限制型平方誤差更提昇0.1db。
根據實驗結果，本論文所提出的新的開關型順序統計濾波器，確實能降低雜訊在低振幅情況的影響，並改善了中值濾波器過度修正(over-correcting)的缺點，而提出的兩種求參數最佳化的方法也能有效提升濾波器的效率。

關鍵字： 限制型LMS，順序統計濾波器

Abstract

During image transmission, digital images are frequently corrupted by noises. Among them, the impulse noise is frequently seen. Different kinds of linear and nonlinear filters have been proposed to remove impulse noises. In recent years, nonlinear filters gradually substituted linear filter in the application of removing impulsive noises. In this thesis, we combine one kind of the nonlinear filter, the median filter, and the fuzzy rules to develop a novel rank order filter mean based switching scheme (NROM-SS) to remove the impulse noises from the images.

While realizing the fuzzy system, it is of most difficulty to find out the fuzzy characteristic. In this study, the fuzzy characteristic is derived based on the differences defined between the current pixel and the rank order value. Specifically, the Laplacian edge detection is also used to produce the fuzzy measurement. Moreover, in order to control the dynamic range of weights of defuzzifier, the weights are optimized using constrained LMS (least mean square) and genie algorithm.

In the design of experiments, 10% to 30% of the low-amplitude uniform-valued and the mixed Gaussian impulsive noises are exploited to test the effectiveness of this method. The experimental results show that the proposed method outperforms the standard median filter by 1~2db in PSNR. The effect of the proposed method becomes better with the rise in noise level. In the experiments using constrained LMS optimization or genie algorithm to estimate the parameters of the filter, the proposed scheme attains 0.4~0.6db improvement in PSNR. In general, the genetic algorithm performs better than the constrained LMS by 0.1db in PSNR.

Based on the experimental results, we conclude that the proposed NROM-SS filter can readily reduce the influence of the low amplitude noises. The drawback of over-correction situation, which is usually observed in the median filter, has been improved with the proposed scheme. Moreover, the two methods for optimal parameter estimation can further improve the effectiveness of the filter.

Keywords- Constrained LMS；Rank order filter mean filter；

目錄

摘要……………………………………………………………………..Ⅰ
Abstract…………………………………………………………………Ⅱ
目錄……………………………………………………………………..Ⅲ
表格……………………………………………………………………..Ⅴ
圖目錄…………………………………………………………………..Ⅵ


第一章 緒論……………………………………………………………..1
1.1前言……………………………………………………………..1
1.2研究動機與目的……………………………………………......1
1.3本文架構………………………………………………………..2
第二章 相關文獻回顧………………………………………………......4
2.1 Rank order mean filter定義……………………………….........4
2.2 ROM-SS濾波器架構…………...…………………..…………..5
2.3拉普拉斯邊緣偵測..………………………………………….....6
2.3.1二次微分邊緣判斷……………………………………………6
2.3.2拉普拉斯運算對於雜訊判斷…………………………………8
第三章 一個新的開關型順序統計平均濾波器……............................10
3.1一個新的ROM-SS………………………………………….....10
3.2一個新的ROM-SS濾波器模糊特徵…………………………11
第四章 設計NROM-SS濾波器……………………………………….13
4.1幾何特徵以及自然語言概念……………….............................13
4.2模糊演算法則系統的設計…….……………………………....17
4.3模糊特徵集合………………………………………………….22
4.4學習演算法…………………………………………………….22
4.4.1限制型最小平方誤差法(Constrained LMS optimization)….24
4.4.2基因演算法(Genetic Algorithm)………………………….....26第五章 實驗設計與實驗結果……………………………………........28
5.1 雜訊模式……………………………………………………...28
5.2 實驗步驟及評估方法…………………………………….......30
5.3 實驗結果……………………………………………………...32
第六章 實驗討論………………………………………………………45
第七章 結論與未來發展………………………………………………47
7.1 結論...........................................................................................47
7.2 未來發展……………………………………………………...47
參考文獻………………………………………………………………..48


表格

表一 模糊法則………………………………………………………15
表二 “Lena” 、“Boat” 和 “Bridge” 影像 並加上雜訊比
30%: 振幅uniform distribution 介於0到120之間...............32
表三 “Lena” 、“Boat” 和 “Bridge” 影像 並加上雜訊
比30%，振幅為固定值100其PSNR的比較………………….36
表四 “Lena” 、“Boat” 和 “Bridge” 影像 並加上雜訊
20%，振幅uniform distribution介於0到255之間，並事
先加上zreomean 雜訊s.d=0.1(mix noise)…………………...38
表五 影像 “Boat”，各個不同的雜訊比，與PSNR(db)
值………………………………………………………………40
表六 “Lena” 實驗結果的PSNR的比較(db)，影像大小
，雜訊機率密度函數p=0.2(20%)灰階值隨機0到255之間..41
表七 複雜度與各個方法的比較……………………………………41
表八 GA參數設定………………………………………………….43
表九 各個訓練方法比較，影像大小 ，雜訊比30%、振
幅0~120……………………………………………………….44

圖目錄

圖2.1 一個從 視窗所觀測的樣本灰階值………………………4
圖2.2 ROM-SS雜訊去除架構圖…………………………………...5
圖2.3.1 a 一個實現(11)所定義之拉普拉斯的濾波器遮罩……………7
圖2.3.1 b 一個實現對角線做拉普拉斯運算濾波器遮罩……………...8
圖2.3.2 a 四個 摺積kernel………………………………………….9
圖3.1 一個新的ROMSS濾波器…………………………………..11
圖4.1. 1 一個NROM-SS濾波器架構……………………………….14
圖4.2. 1 模糊系統的模糊化與解模糊化對於模糊引擎的基本架構.17
圖4.2. 2 一個三輸入一輸出的模糊系統…………………………….18
圖4.2. 3 歸屬函數於very small、small和large……………………..20
圖4.3. 1 (a)自然語言變數 與u、v曲面關係圖(2-D維度)(b)自然
語言變數 與z曲面關係圖圖(1-D維度)…………………22
圖4.4 .1 (a)一個1-D step-type 函數其自然語言large
(b)一個1-D step-type 函數其自然語言small …………….23
圖5.1. 1 型式一雜訊( 表示有雜訊， 沒有雜
訊， 為一uniform distribution 振幅)……….29
圖5.2. 1 原始影像(a)Lena (b)Boat (c)Bridge………………………...31
圖5.3. 1 “Lean”圖(a)雜訊比30%振幅0~120(uniform distribution)
(b)NROM-SS濾波器(26.89db)(c)開關型中值濾器(24.81db)
(SWM) (d) ROM-SS濾波器(25.07db) (e)LUM濾波器
(24,87db) (f)高機率雜訊去除濾波器(22.09db)……………33
圖5.3. 2 “Boat”圖(a)雜訊比30%振幅固定100(b)NROM-SS濾波
器(20.23db)(c) ROM-SS濾波器(19.01db)(d)開關型中值
濾波器(18.32db)(e) LUM濾波器(f) 高機率雜訊去除濾
波器(16.89db)………………………………………………35
圖5.3.3 “ Lean”圖(a)雜訊比20%其振幅uniform distribution
介於0到255之間和zero means.d=0.1(mixnoise)
(b)NROM-SS濾波器(25.97db)(c)ROM-SS濾波
(24.21db)(d)開關型中值濾波器(24.17db) (e)高機率雜
訊去除濾波器(20.71db) (f)LUM濾波器(24.06db)………..37
圖5.3.4 (a)一張訓練影像 “Goldhill”(b)NROM-SS訓練之後測
試Boat”雜訊比20%(25.17db)(c)開關型中值濾波器
SWM訊比(25.03db)(d)LUM濾波器(24.93db)(e)高機率
雜訊去除濾波器20%(24.31db).……………………………39
圖5.3.5 (a)一張影p=0.2(20%)“Lena”(b)N-ROMSS濾波器
(33.36db)(c)開關型中值濾波器(SWM)(32.26db)
(d)ROM-SS濾波器(33.41db)(e)高機率雜訊去除濾
波器(26.13db) (f)LUM濾波器(31.10db)…………………..42

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