正子斷層攝影(Positron Emission Tomography, PET)的光子衰減效應，可利用一外部的正子發射源進行穿透式掃描以完成衰減校正。臨床上，穿透式掃描多在病人注射正子衰變藥物之後進行。因此，掃描儀內放射性活度的增加，造成穿透式掃描資料偏差。本研究將建立注射正子藥物後穿透式掃描的資料模型，藉以模擬掃描儀所獲得的資料，並結合Luk以及Zaers等人的方法，以臨床上方便實行且準確的評估法，得到資料模型內的雜訊元素量。根據此資料模型，使用前調式共軛梯度法(Preconditioned conjugate gradient method)計算最大事後機率評估(Maximum a posteriori，MAP)，以重建注射正子藥物後穿透式掃描(Post-injection transmission scan)影像。臨床應用的評量，是根據CTI/Siemens PET scanner ECAT EXACT HR+所得之穿透式掃描資料進行影像重建，影像重建的結果依照肺、軟組織和骨頭三個區域所圈出之ROI (Regions of interest)，分別計算ROI內的影像平均值與標準差。實驗結果顯示，本研究的資料模型及雜訊評估方法所重建的穿透式影像，相較於傳統的方法，更接近理想上511keV之線性衰減係數值。

By using an external source, attenuation correction in positron emission tomography (PET) can be achieved by measuring a transmission scan, and then calculated the ratio of blank scan and transmission scan data as attenuation correction factors (ACFs). In order to increase throughput of scanners and to reduce motion artifacts, post-injection transmission scans are widely used in clinical routine. However, the additional radiotracer activities in the scanner’s field of view contributed from patient can lead to a biased calculation of ACFs. To improve the accuracy of ACFs, another feasible approach is to reconstruct transmission image and then calculate the ACFs by forward projecting the transmission image. In this research, a joint Poisson model of post-injection transmission scan is proposed to incorporate true transmission data as well as noises including random events and cross-contamination from the emission events of the patient. Based on the proposed model, the transmission image is then reconstructed using a pre-condition conjugate gradient algorithm under the paradigm of maximum a posteriori estimation. We use clinical data acquired from a CTI EXACT HR+ scanner for model validation. The experimental results have indicated that the voxel values of reconstructed transmission image are close to those ones of linear attenuation coefficients at 511KeV photon. The proposed image reconstruction method for post-injection transmission scan can result in generation of more accurate ACFs and lead to improvement of PET quantitation.

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