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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 周呈霙(Cheng-Ying Chou) | |
dc.contributor.author | Hsi-Hao Chao | en |
dc.contributor.author | 趙希皓 | zh_TW |
dc.date.accessioned | 2021-06-17T02:30:43Z | - |
dc.date.available | 2022-08-24 | |
dc.date.copyright | 2017-08-24 | |
dc.date.issued | 2017 | |
dc.date.submitted | 2017-08-18 | |
dc.identifier.citation | Hestenes, M. R., & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems (Vol. 49): NBS.
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/68689 | - |
dc.description.abstract | 小動物正子斷層掃描系統為近期經常被使用之PET系統,因醫學相關之研究均須經過動物實驗作為是否能用於人類之依據之一,故本研究使用小動物環形PET系統。醫學臨床上多使用濾波反投影作為影像重建之解析式重建法,但重建之影像品質較差,而疊代式重建法之優點為能夠引入解析式重建法之物理因素,使影像品質更好。本研究使用了MATLAB繪製無雜訊假影以確認重建演算法正確,並透過OpenGATE模擬真實環形PET系統,期望重建之影像能與真實影像接近。重建演算法之系統矩陣使用射束追蹤法計算光子經過互毀效應被偵檢器接收到之路徑長。
共軛梯度法(CG)為一般常見之求解最小平方誤差之最佳化演算法,但由於其需計算系統矩陣之轉置矩陣,當重建之系統過大時會使計算時間增加並增加運算複雜度,Chambolle與Pock提出使用原始-對偶最佳化演算法之CP演算法,也能夠求解最小平方誤差,其優勢為計算簡易。而結果雖然CG收斂速度較CP迅速,但隨著疊代次數增加,雜訊也隨之增加。並將CP結合總變異最小化,將影像邊緣保留與降低雜訊,並且透過方均根誤差、條件原始-對偶間距判斷影像品質與收斂程度。並提出可旋轉式稀疏掃描系統,期望能重建出與完整掃描系統相似之影像。 | zh_TW |
dc.description.abstract | The small animal ring PET system is frequently used nowadays. Medical-related studies are subject to animal experiments as a basis for the use on humans. Clinical reconstruction often use the filter back-projection as the image reconstruction method. But due to the worse image quality, the iterative reconstruction method can perform better than the analytic reconstruction because it can introduce the physical factors during the reconstruction. In this study, we simulate the noise-free data using the MATLAB to check our algorithm implementation. In addition to use digital phantom, we also used OpenGATE to simulate the real ring PET system. Furthermore, we used ray tracing to calculate photon traveling path to build system matrix.
Conjugate gradient and Chambolle and Pock are optimization algorithms for solving the least squares problem. The advantage of CP algorithm is simple to implementation. The result show that although the convergence rate of CG is faster than that of CP, but the noise is getting larger. On the other hand, CP have a simple way to combine to the total variance penalty term in order to preserve the edge. Moreover, we incorporated the normalized mean square error and cPD to check the convergence. At last, we compare image quality of the full scan and sparse scan system. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T02:30:43Z (GMT). No. of bitstreams: 1 ntu-106-R04631017-1.pdf: 14656165 bytes, checksum: 5ceeb959892eb8a1724ea3a0ca6cbf85 (MD5) Previous issue date: 2017 | en |
dc.description.tableofcontents | 口試委員會審定書 i
致謝 ii 摘要 iii Abstract iv 目錄 v 圖目錄 vii 第一章 前言 1 第二章 文獻探討 3 2.1 正子放射斷層造影 (Positron Emission Tomography, PET) 3 2.1.1 原理 3 2.1.2 雜訊之產生 5 2.2 模擬與重建演算法 6 2.2.1 GEANT4於放射斷層掃描之應用 6 2.2.2 PET影像重建之基本原理 7 2.2.3 最大近似最大期望值法 (Maximum Likelihood Expectation Maximization, MLEM) 9 2.2.4 共軛梯度最佳化演算法 (Conjugate Gradient Optimization Algorithms) 10 2.2.5 原始-對偶最佳化演算法 (Primal-Dual Optimization Algorithm) 11 2.2.6 總變異最小化 (Total Variation Minimization Algorithm) 14 2.2.7 系統矩陣 15 第三章、 材料與方法 16 3.1 實驗架構 16 3.2 模擬PET之硬體資訊 17 3.3 LOR資訊整理 18 3.4 系統矩陣之建立 20 3.5 最大相似度函數 20 3.6 最大近似最大期望值法 (Maximum Likelihood Expectation Maximization, MLEM) 22 3.7 共軛梯度最佳化演算法 (Conjugate Gradient Optimization Algorithms) 23 3.8 原始-對偶最佳化演算法 24 3.8.1最小平方誤差 25 3.8.2最小平方誤差與非負限制 28 3.8.3最小平方誤差與總變異數最小化 29 第四章、結果與討論 32 4.1 模擬之假體 32 4.2 評估影像指標 33 4.3 最小平方誤差重建 33 4.3.1 無雜訊影像重建 33 4.3.2 共軛梯度法(CG)與Chambolle Pock(CP)演算法 35 4.3.3 Chambolle Pock + 總變異最小化 37 4.3.4 Chambolle Pock + 總變異最小化之縮小 值 41 4.3.5 CP-TV於完整與稀疏掃描系統 44 第五章、結論 46 第六章、參考文獻 48 | |
dc.language.iso | zh-TW | |
dc.title | 可旋轉式小動物正子斷層掃描系統之影像重建 | zh_TW |
dc.title | Image Reconstruction for the Configurable Small-Animal Ring PET System | en |
dc.type | Thesis | |
dc.date.schoolyear | 105-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 許靖涵(Ching-Han Hsu),蕭穎聰(Ying-Tsung Hsiao) | |
dc.subject.keyword | 正子斷層掃描,共軛梯度法,原始-對偶演算法,總變異最小化, | zh_TW |
dc.subject.keyword | PET,Conjugate Gradient,Chambolle Pock algorithm,Total Variance, | en |
dc.relation.page | 49 | |
dc.identifier.doi | 10.6342/NTU201703344 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2017-08-18 | |
dc.contributor.author-college | 生物資源暨農學院 | zh_TW |
dc.contributor.author-dept | 生物產業機電工程學研究所 | zh_TW |
顯示於系所單位: | 生物機電工程學系 |
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