臺灣博碩士論文加值系統

影像重建在單光子發射性斷層攝影(SPECT)及正子斷層攝影(PET)中是重要程序，目前常用的影像重建法有兩種，第一為反投影法，第二為疊代法。反投影法速度較快，但星狀假影問題等為其缺點；而疊代式重建法(MLEM及OSEM)可以排除假影問題，卻需要大量電腦資源如記憶體、CPU運算時間，隨著近年科技快速發展這些缺點變的較不重要，由於斷層攝影收集資料的不完整性問題，使得微量的雜訊在影像重建過程中也會放大。
機率矩陣為統計型影像重建法中重要核心，機率矩陣包含著接收資料與未知影像間關係以及幾何效應、衰減效應、偵測效率…等物理效應。正確的機率矩陣影響著影像重建的速度與精確度。
本研究提出一新方法，正交參照法(OCR)重新計算機率矩陣，OCR假定當收到的投影資料是零時，其對應到要計算的像素都沒有光子，所以像素機率值相對應到零值投影資料就設定為零。此方法先參照正交方向投影資料來計算機率矩陣，每當正交投影資料為零，其對應像素機率值設定為零。再用得到的新機率矩陣來做MLEM和OSEM影像重建。研究結果顯示用OCR方式確增加加速影像收斂速度及減少影像發散。OCR方式可應用在SPECT與PET 影像重建。

Image reconstruction is the key procedure in single photon emission
computed tomography (SPECT) and positron emission computed tomography
(PET). There are two basic approaches to reconstruct the image raw data.
The first method is filtered backprojection (FBP) ,the second is iterative reconstruction. Convenience and relative high calculation speed are the major concerns of FBP, but the star artifact which caused by FBP is the inherent weak point. On the other hand, star artifacts can be eliminated by iterative method (MELM and OSEM). Iterative method requires a lot of computer resources, such as memory space and CPU time, but it becomes less serious in recent years for the rapid development of advance technologies of compute science. Due to the incomplete image data obtained by gamma camera, the noises are always amplified during the iterative computations.

Probability matrix is the major part of statistical image reconstruction methods. Probability matrixes hold the relationships between the acquired image data and unknown images, geometric effect, attenuation effect and detection efficiency. The correctness of the probability matrix would play an important role of accuracy and speed of reconstruction methods.

In this study we proposed a new method ‘Orthogonal cross reference, OCR’. It is reasonable to assume that whenever a projection datum is zero, the related pixels in calculation do not emit any photons. So the probability of the pixels related to the zero projection datum must set to zero. In this method, first we recalculate the probability matrix of pixels referred to the orthogonal projection data. Whenever there is a zero orthogonal projection datum, the probabilities of the related pixels are set to 0. We then reconstruct the image by MELM and OSEM according to the new probability matrix.

By the OCR method, we found that the convergent speed of image reconstruction was enhanced and the noise divergent was diminished in both MLEM and OSEM. Also, this new method can be apply to both SPECT and PET.

中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………Ⅱ
目錄……………………………………………………………………Ⅲ
圖索引…………………………………………………………………V

第一章 續論………………………………………………………… 1
1.1研究動機……………………………………………………… 1
第二章 核醫影像重建法………………………………………………3
2.1單光子電腦斷層掃描…………………………………………7
2.2最大概似函數估算…………………………………………… 7
2.3最大概似與期望值最大演算法……………………………… 8
2.4序列子集值期望最大值演算法……………………………… 13
第三章 材料與方法……………………………………………………19
3.1機率矩陣的建立……………………………………………… 21
3.2新機率矩陣計算……………………………………………… 29
3.3實驗材料……………………………………………………… 31
第四章 結果與討論……………………………………………………34
4.1結果…………………………………………………………… 34
4.2討論…………………………………………………………… 46
4.3未來展望……………………………………………………… 48
參考文獻……………………………………………………………… 49
附錄…………………………………………………………………… 53

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