以區塊為基礎的影像去雜訊研究｜國立清華大學博碩士論文庫

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研究生：	蕭佩琪 Hsiao, Pei-Chi
論文名稱：	以區塊為基礎的影像去雜訊研究 A Study on Patch-Based Image Denoising Methods
指導教授：	張隆紋 Chang, Long-Wen
口試委員:	廖弘源張寶基陳朝欽賴尚宏陳煥宗張隆紋
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 資訊系統與應用研究所 Institute of Information Systems and Applications
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	97
中文關鍵詞：	聯盟賽局、優勢集合、非局部均化、影像去雜訊、成對資料分群、主成分分析、機率模型、聚合式分群
外文關鍵詞：	coalitional games, dominant sets, nonlocal means, image denoising, pairwise data clustering, principal component analysis, probability model, agglomerative clustering
相關次數：	點閱：2 下載：0
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自然影像可視為由一群富含資訊的影像區塊所構成，在本論文裡，我們利用相似紋理特徵的影像區塊們進行去雜訊研究。近年來，非局部均化的去雜訊方法受到了很多重視，它是透過鄰近像素點的加權平均來得到去雜訊後的估測值，其中權重的決定方式是根據影像區塊間的相似度。我們提出以影像區塊的相似度為基礎進行像素點分群，從鄰近像素點篩選出相似的子集合進行均化，使之能達到最佳的去雜訊效果並同時保留影像細節。我們設計一聯盟賽局模型來解分群問題，將每一雜訊像素視為玩家，以影像區塊間的相似度作為倆倆玩家彼此合作的報償，經由我們所提出的背叛與孤立規則，每個玩家可以經由參與不同的聯盟來提高自身的獲利，在這樣的機制下，我們可以獲得最佳與穩定的聯盟，而其中的玩家們彼此具有高度的相似度，將其用於非局部均化以去除雜訊。另外，我們也提出頻率域去雜訊的方法，讓去雜訊影像在輪廓線條有較佳的表現。我們首先將雜訊影像分割成重疊的影像區塊，再透過聚合式分群影像區塊們，再者，我們利用機率主成分分析每一群雜訊的影像區塊，並估測去雜訊後的影像區塊以重建影像。藉由廣泛的實驗，我們證明所提出的兩種去雜訊方法能有效地達到影像恢復的目的。

Image patches are considered as the fundamental building blocks of an image. In this dissertation, the restoration of a noisy image based on its redundant patches is studied. Nonlocal means (NLM) is known as a weighted average filtering based on patch similarity. We propose to improve NLM by only including a cluster of pixels with mutually similar patch appearances to that of the pixel to be denoised. A coalitional game model is designed to find an optimal cluster of pixels for every noisy pixel. In the coalitional game model, each pixel is treated as a player and each player receives a payoff which depends on the mutuality among players in the same group. Therefore, pixels with similar patch appearances are prone to group together for cooperation. We propose betrayal and hermit rules to describe the cooperative behaviors among the players and apply it to find the optimal and stable group of pixels for the denoising purpose. In addition, stability analysis of our coalitional game model is given. Besides, we propose an alternative patch-based approach, which suppresses the image noise by shrinkage of coefficients in transform domain. We first sample overlapped patches from the noisy image and then cluster them into many similar groups. For every group of noisy patches, we apply probabilistic principal component analysis (PPCA) to denoised jointly in the learnt PCA domain. Putting back the denoised patches to their original positions, the denoised image is then reconstructed. Our two patch-based denoising approaches are shown to be effective in removing the image noise while maintaining the edge structures of the original noise-free images. The superior performances are shown by both visual and quantitative qualities.

摘要                                                                               ix
Abstract                                                                          xi
List of Figures                                                                 xvii
List of Tables                                                                 xxiii
Introduction                                                                     1
1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Overview of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Adaptive Nonlocal Means Filter . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Clustering Using Cooperative Game . . . . . . . . . . . . . . . . . . . . . .4
2.3 Transform-Domain Coefficient Shrinkage . . . . . . . . . . . . . . . . . . . 5
3 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Background                                                                       9
1 Adaptive Nonlocal Means Filter . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Coalition Formation Games . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Transform-Domain Coefficient Shrinkage . . . . . . . . . . . . . . . . . . . .17
Dominant Sets in Coalitional Game                                               21
1 Introduction to Graph Partition . . . . . . . . . . . . . . . . . . . . . . . 21
2 Coalitional Games for Graph Partition . . . . . . . . . . . . . . . . . . . . 23
2.1 Dominant Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 General Coalitional Game . . . . . . . . . . . . . . . . . . . . . . . . . .26
2.3 Coalitional Subgame . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Stability of Coalitional Games . . . . . . . . . . . . . . . . . . . . . . . .36
Image Denoising with Dominant Sets by a Coalitional Game Approach               41
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
2 Dominant-Set-Expansion Algorithm . . . . . . . . . . . . . . . . . . . . . . .43
3 Texture Image Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Image Denoising with Dominant Sets . . . . . . . . . . . . . . . . . . . . . .47
5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Transform-Domain Patch-Based Image Denoising Using Probabilistic
 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 61
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
2 Denoising Algorithm of Patch Clustering and Collaborative Filtering . . . . . 62
2.1 Noisy Patch Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . .63
2.2 PPCA-Based Image Denoising . . . . . . . . . . . . . . . . . . . . . . . . .64
2.3 Dynamic Dimensionality Reduction . . . . . . . . . . . . . . . . . . . . . .66
2.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3 LMMSE-Based Image Denoising . . . . . . . . . . . . . . . . . . . . . . . . . 67
4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
Conclusion                                                                      81
A Deriving Linear Minimum Mean Square-Error (LMMSE) Estimator                     83
B Graph Partition in Figure 3.3                                                   85
Bibliography                                                                      87
Publications                                                                      95

                                

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