正子斷層掃描之快速交互參照式最大概似估計

Abstract

正子斷層掃描（PET）可以診察出人體內部新陳代謝活動的情形。因 此，它提供了 醫療診斷重要的資訊。而新陳代謝的強度是由置於人體 外部的偵測器所間接觀測到的。 用間接的觀測值來重建實際的影像， 這是一種典型的統計逆向問題。由於這種問題解的 不良性，所以，沒 有正則化的PET影像將會有雜訊及邊界的假象。這是PET 的能力限制， 並不能藉由改良儀器設計來解決。所以為了要有較好的重建影像，我們需 要去考慮專家 的見解或其它的斷層掃描系統，例如：X-ray CT, MRI等 掃描器，所提供的相關資訊。 相關的邊界資訊可以提供有用的訊 息。但是因為解剖學上的人體器官構造與實際的新 陳代謝情形並不盡相 同，所以邊界資訊可能是不完全的或是不正確的。因此交互參照是重 要 而明智的。我們考慮有偶發事件及衰減情形的PET，研究交互參照式的最 大概似估計重 建法，並以修改後的演算法來處理。特別是，我們建議快 速、有效、穩健的方法去抽取相 關但不完全的邊界資訊來重建影像。並 且利用修正後的ECM及SAGE演算法來加快計算速度 。此外，利用資料及 廣義近似交叉確認準則，則可很快地來選擇權衡參數。從不同例子的模擬 中驗證了這種加速互相參照式最大概似估計的表現是實際且可行的。 Positron emission tomography (PET) can explore the in vivo metabolic activit y inside a human body, which provides important information for medical diagnosis. The intensity of metabolic activity is indirectly observed through the scintillation detectors outside a human body. The reconstr uction from indirect observations to a target image is a typical problem in statistical inverse problem. Due to the inherent ill-posedness of stat istical inverse problems, the reconstruction images of PET without regularizat ion willhave noise and edge artifacts. This is the limit of PET which can not be resolved from the improvement of instrumental designs. In order to hav e betterreconstruction images, it is necessary to borrow the strength from the relatedinformation from expertise or other tomography systems, such as X-ray CT scan,MRI, and so forth. The correlated boundary information may offer the useful information in reducing the noise and edge artifacts. However, the boundary informati on may be incomplete or incorrect since the anatomy boundaries are different from thefunctional ones. Thus, cross-reference is important to make use of the boundary information wisely. We will study the cross-reference maximum likelihood estimate with the adapted EM algorithm for PET in the prese nce of accidental coincidence events and attenuation. In particular, speedy, efficient and robust approaches are proposed to extract the related bu t incomplete boundary information. Fast algorithms adapted from expectat ion/ conditional maximization and space alternating generalized expectation maximization are proposed to accelerate the computation. The method of generalized approximate cross validation is applied to select penalty parameter from observation data quickly. The Monte Carlo studies demon strate the improvement.