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博碩士論文 etd-0910108-123728 詳細資訊
Title page for etd-0910108-123728
論文名稱
Title
馬可夫影像場針對模糊影像還原的研究
Study of the Image restoration for blurred Markov field images
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
80
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2008-07-30
繳交日期
Date of Submission
2008-09-10
關鍵字
Keywords
馬可夫影像場
Markov field images
統計
Statistics
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中文摘要
中文摘要
在自然界的系統模型描述一般都以因果性系統居多,就是過去只會對未來造成影響。相對的非因果性系統,就是過去、現在、未來都會互相有關,探討的部分就比較少,本論文即是針對非因果性系統下受到信號間互相干擾以及加成雜訊影響之信號還原之探討。
本系統應用到影像還原上,在馬可夫影像還原的模型中並沒有考慮模糊影像的情況,而卡門濾波器的模型中雖有針對模糊影像的還原,卻沒有影像場的概念,所以我們希望利用馬可夫影像場的觀念搭配上卡門濾波器來針對模糊影像加上加成雜訊來做影像還原,在卡門濾波器中我們藉著動態方程式改寫成因果性形式以獲取卡門濾波器所需的參數,再利用馬可夫影像場的影像參數來取得區域的生成雜訊變異數以及像素與生成雜訊之相關性矩陣,而在論文中我們先對一般影像加上加成雜訊來做還原,接著推廣成對模糊影像加上加成雜訊的影像還原,另外我們也對估測模糊圖的生成雜訊有較深入的探討,最後我們比較三種影像還原(1).複合高斯馬可夫隨機場(2).卡門濾波器(3).馬可夫影像場的卡門濾波器對模糊影像的還原情況,我們發現使用馬可影像場的卡門濾波器有較好的還原效果。
Abstract
Abstract
A naturally system is usually modeled as a causal system, in which the present output is determined by the past inputs. In contrast, the noncausal system is modeled by the future inputs in addition to the past inputs, and is also less explored. In this thesis, we apply the noncausal modeling to the image restoration for the blurred images corrupted by additive white Gaussian noise.

We applied three methods for our image deblurring problem. The first method is exploiting the compound Gauss-Markov image model, which has been proven useful in image restoration. The image is restored in two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field. The second method is to apply the Kalman filter using the above the compound Gauss-Markov image model and the line field. The third method is to apply the Kalman filter without using the line field. Our experiments have shown the second method to be the best among the three methods.
目次 Table of Contents
目 錄
第一章 序論……………………………………………………………1

第二章 一維卡門濾波器………………………………………………3
2-1一維卡門濾波器……………………………………… 3
2-2在非因果性模型下的卡門濾波器………………… 7

第三章非因果性動態方程式的應用:影像還原………………………10
3-1 影像模型簡介…………………………………………… 10
3-2 複合高斯馬可夫隨機場理論回顧……………………… 12
3-2-1聯合最大後置機率(MAP)的估測… 13
3-2-2複合高斯馬可夫模型之參數……………17
3-3 基於非因果性模型之影像還原………………………… 20
3-3-1 影像分割………………………………………… 20
3-3-2 取得增益矩陣以及生成雜訊變異數…24
3-4二維卡門濾波器……………………………………………27
3-5卡門公式簡化推導…………………………………………32

第四章 馬可夫影像場針對模糊影像還原的研究………………………39
4-1 模糊影像模型………………………………………………39
4-2 模糊影像生成雜訊之估測…………………………………43
4-3卡門模糊影像公式簡化推導…………………………………47

第五章 求反模糊矩陣……………………………………………… 56
5-1 求區域模糊反矩陣……………………………………………56
5-2 Minimal Solution…………………………………58
5-3反模糊矩陣還原方法改進…………………………………59


第六章 模糊影像實驗結果……………………………………………… 61

第七章 結論……………………………………………………………… 72

參考文獻……………………………………………………………………73
參考文獻 References
參考文獻
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