臺灣博碩士論文加值系統

貝氏定理影像重建演算法是1990年Green將最大相似度評估法和最大事後機率評估法結合所產生的一步延遲期望值最大演算法(One-Step-Late Expectation Maximum, OSL)，使用在正子斷層掃描上進行影像重建時可以搭配不同的影像事前機率(Image prior)來做不同方式的雜訊抑制，但在這個過程中影像事前機率的影響有可能會使重建影像過度平滑(over-smoothing)或是在邊緣部分產生其他問題。飛行時間正子斷層掃描(Time-of-Flight PET)能提供互毀光子被偵檢器接收到的時間差，增加重建影像的解析度，提升影像訊雜比。在本研究中提出將貝氏定理影像重建演算法用於重建TOF PET影像，包含TOF-OSL與TOF-OSEM-OSL重建法，並和傳統PET使用OSL與OSEM-OSL重建法所重建的影像做比較，利用TOF技術改善貝氏定理影像重建法的缺點，在保留影像事前機率的貢獻下，增加了TOF的時間資訊優勢，進而提升影像品質。

A Bayesian image reconstruction algorithm, One-Step-Late (OSL) algorithm which combines maximum likelihood expectation maximization (MLEM) with maximum a posteriori (MAP) estimation, was derived by Green in 1990. In Positron emission tomography (PET), image reconstruction using OSL combines the likelihood function with image prior. Use different way to reduce the effect of noise in the data with different image prior. However, image prior may over-smooth small objects and edges. Time-of-Flight PET system can provide time difference of annihilation photon pair and this TOF characteristic can improve image resolution and signal-to-noise ratio (SNR). In this study, we proposed a TOF iterative image reconstruction algorithm based on the Bayesian scheme. Using TOF technique can improve the image quality of image which reconstructed by Bayesian image reconstruction algorithm. The results of TOF-OSL and TOF-OSEM-OSL would be compared with the results of OSL and OSEM-OSL. TOF Bayesian image reconstruction algorithm can provide not only noise reduction but also can improve the image quality in PET.

第一章 前言…………………………………………………………..…1
第二章 正子斷層掃描…………………………………………………..5
2-1成像原理………………….……………………………………..5
2-2影響成像的物理因素…….……………………………………..6
2-3訊號收集與排列………….…………………………………..…7
2-4傳統疊代式影像重建…………………………………………...8
2-4.1資料模型…………………………………………………..8
2-4.2最大相似度評估…………………………………..............9
2-4.3最大相似度期望值最大演算法………………………....10
2-4.4序列子集期望值最大演算法…………………..………..11
2-5貝氏定理於影像重建中的運用……………………………….12
2-5.1最大事後機率評估法…………..………………………..12
2-5.2一步延遲期望值最大演算法…………………..………..13
2-5.3吉布斯分布………………………………………………14
2-5.4最大懲罰相似度評估………..…………………………..15
2-5.5影像事前機率……………………………………………15
第三章 飛行時間正子斷層掃描………………………………………18
3-1 TOF PET 系統發展………………………………………........18
3-2飛行時間(Time-of-Flight)技術原理…………………………...19
3-3偵測機率矩陣………………………………………………….21
3-3.1空間幾何關係機率矩陣…………………………………21
3-3.2時間解析度機率分布……………………………………22
3-3.3 TOF PET 機率矩陣……………………………………..24
3-4 TOF PET的優勢……………………………………………….26
第四章 TOF PET影像重建法…………………………………………30
4-1 TOF影像重建發展…………………………………………….30
4-2偵收光子期望值……………………….………………………31
4-3 TOF最大相似度評估………………………………………….32
4-4 TOF PET最大相似度期望值最大演算法…………………….34
4-5 TOF PET序列子集期望值最大演算法……………………….36
4-6 TOF最大事後機率評估與最大懲罰相似度函數…………….38
4-7 TOF PET一步延遲期望值最大演算法……………………….40
4-8 TOF PET序列子集一步延遲期望值最大演算法…………….41
第五章 實驗設計………………………………………………………42
5-1實驗平台…………………………………………………….....43
5-2假體設計……….………………………………………………45
5-3 PET正弦圖…………………………………………………….46
5-4影像指標……………………………………………………….47
第六章 實驗結果與討論………………………………………………50
6-1傳統PET和TOF PET之演算法驗證實驗………………….....50
6-1.1無帕松雜訊模擬實驗……………………………………50
6-1.2加入帕松雜訊模擬實驗…………………………………56
6-2貝氏定理用於TOF與Non-TOF影像重建實驗………………62
6-2.1 Quadratic事前機率…………………………………...…67
6-2.2 L1-Norm事前機率………………………………………75
6-2.3 Huber事前機率………………………………………….83
6-2.4 Geman and McClure事前機率………………………….91
6-2.5 Relative difference事前機率……………………………99
6-3 綜合討論……………………………………………………..108
第七章 結論與未來方向……………………………………………..112
參考文獻………………………………………………………………114

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