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基于壓縮傳感原理的圖像重建方法研究電子書
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資料類別
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電子電工畢業(yè)論文（設(shè)計(jì)） |
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課程(專業(yè))
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電路與系統(tǒng) |
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關(guān)鍵詞
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壓縮傳感|圖像重建 |
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適用年級(jí)
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大學(xué) |
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身份要求
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普通會(huì)員 |
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金 幣
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30 �。�金幣如何獲得？） |
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pdf |
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1969K |
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發(fā)布時(shí)間
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2009-05-19 21:17:00 |
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預(yù)覽文件
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無(wú) |
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下載次數(shù)
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15 |
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lcw |
內(nèi)容簡(jiǎn)介：
基于壓縮傳感原理的圖像重建方法研究電子書
摘 要
傳統(tǒng)的Nyquist 采樣定理要求采樣頻率必須大于等于信號(hào)最高頻率的兩倍，但很多情況下信號(hào)帶寬較大，采樣頻率達(dá)不到最高頻率的兩倍。最近Donoho 和Candès 提出了壓縮傳感CS(Compressed Sensing)理論。該理論利用原始信號(hào)或圖像的稀疏性先驗(yàn)知識(shí)，通過(guò)合適的優(yōu)化算法，可由少量的采樣值或觀測(cè)值來(lái)進(jìn)行重建。目前該理論的研究尚處于初級(jí)階段，大多是基于壓縮傳感基礎(chǔ)理論的研究和一維信號(hào)的重建。本文將壓縮傳感理論應(yīng)用于圖像重建中，針對(duì)其重建速度慢和重建質(zhì)量不高的缺點(diǎn)，在深入研究現(xiàn)有算法的基礎(chǔ)上，從以下幾方面進(jìn)行研究：(1)基于壓縮傳感和代數(shù)重建法的CT(Computed Tomography)重建 結(jié)合壓縮傳感理論提出了一種基于代數(shù)重建法ART(Algebraic ReconstructionTechnique)的高質(zhì)量CT 圖像重建算法。該算法將CT 圖像的梯度稀疏性結(jié)合到ART 圖像重建中，在每次迭代中的投影操作結(jié)束后用梯度下降法調(diào)整全變差，減小圖像梯度的l1范數(shù)。實(shí)驗(yàn)結(jié)果表明了該算法的有效性。(2)基于全變差多種范數(shù)的核磁共振圖像重建 利用核磁共振圖像具有梯度和邊緣稀疏性的先驗(yàn)知識(shí)來(lái)加快其成像速度，提出了一種基于全變差的核磁共振圖像重建算法，并對(duì)l1、l p ( 0 ﹤ p ﹤1)與log和懲罰函數(shù)三種范數(shù)進(jìn)行了實(shí)驗(yàn)和比較分析。(3)基于線性Bregman 和混合基稀疏表示的壓縮傳感圖像重建 提出了一種基于離散余弦變換和雙樹復(fù)數(shù)小波兩種基混合的圖像稀疏表示，利用線性Bregman 迭代來(lái)進(jìn)行重建的壓縮傳感系統(tǒng)。該算法在每一次迭代更新后用梯度下降法進(jìn)行全變差調(diào)整，再分別在兩種基上執(zhí)行軟閾值處理來(lái)減小圖像的l1范數(shù)。實(shí)驗(yàn)結(jié)果表明該算法有效提高了重建圖像的質(zhì)量。
關(guān)鍵詞 壓縮傳感；圖像重建；稀疏表示；全變差調(diào)整；代數(shù)重建法；線性
目 錄
摘要···················································································································· I
Abstract············································································································· II
第1 章 緒論·······································································································1
1.1 研究背景·································································································1
1.2 國(guó)內(nèi)外研究現(xiàn)狀·····················································································1
1.2.1 壓縮傳感重建算法概述····································································2
1.2.2 壓縮傳感應(yīng)用概述···········································································3
1.3 本文研究的內(nèi)容·····················································································4
1.4 本文的結(jié)構(gòu)安排·····················································································5
第2 章 壓縮傳感圖像重建···············································································6
2.1 壓縮傳感理論·························································································6
2.2 稀疏性·····································································································7
2.3 隨機(jī)投影·································································································8
2.3.1 限制等容性·······················································································8
2.3.2 不相干性·························································································10
2.4 圖像重建方程·······················································································11
2.5 本章小結(jié)·······························································································12
第3 章 基于壓縮傳感和代數(shù)重建法的CT 重建···········································13
3.1 CT 簡(jiǎn)介·································································································13
3.2 代數(shù)重建法···························································································14
3.2.1 代數(shù)重建法原理·············································································14
3.2.2 代數(shù)重建法的影響因素分析··························································15
3.3 全變差調(diào)整···························································································17
3.4 基于ART 和壓縮傳感的CT 重建算法···············································19
3.5 實(shí)驗(yàn)結(jié)果分析和比較···········································································21
3.6 本章小結(jié)·······························································································28
第4 章 基于全變差多種范數(shù)的MR 圖像重建··············································29
4.1 MRI 簡(jiǎn)介·······························································································29
4.2 基于多種范數(shù)的MR 圖像CS 重建·····················································30
4.2.1 MRI 的CS 不相干采樣··································································30
燕山大學(xué)工學(xué)碩士學(xué)位論文
VI
4.2.2 基于三種范數(shù)的壓縮傳感MRI 重建············································30
4.3 MR 圖像重建算法················································································32
4.4 實(shí)驗(yàn)結(jié)果分析及其比較········································································34
4.5 本章小結(jié)·······························································································40
第5 章 基于線性Bregman 和混合基稀疏表示的壓縮傳感圖像重建··········41
5.1 基于DCT 和DTCWT 混合基稀疏表示的壓縮傳感··························41
5.1.1 基于混合基稀疏表示的壓縮傳感重建··········································41
5.1.2 DTCWT 和DCT 簡(jiǎn)介····································································42
5.2 線性Bregman 迭代算法及其分析·······················································44
5.3 基于混合基稀疏表示的線性Bregman 迭代·······································46
5.4 基于DCT 和DTCWT 混合基稀疏表示的CS 系統(tǒng)實(shí)現(xiàn)···················48
5.5 實(shí)驗(yàn)結(jié)果分析和比較···········································································50
5.6 本章小結(jié)·······························································································54
結(jié)論··················································································································55
參考文獻(xiàn)··········································································································57
攻讀碩士學(xué)位期間承擔(dān)的科研任務(wù)與主要成果············································63
致謝··················································································································64
作者簡(jiǎn)介··········································································································65
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