正子斷層掃瞄核醫影像因為受到解析度較低的限制，導致影像受到部分容積效性(Partial Volume Effect)發生，進而影響影像準確定量的優點。為了修正部分容積效應，Rousset於1998年提出GTM(Geometry Transfer Matrix)方法，應用於校正腦部影像的部分容積效應，成功恢復影像中受到部分容積效應影響的腦部區域活度。然而，因為GTM方法必須要配合相對的解剖性影像譬如MRI、CT進行影像對位，所以在執行的過程中，會因為影像對位以及影像分割的不準確，影響校正結果。故本論文以GTM演算法為基礎，去除需要解剖性影像的對位與分割步驟，進而完成部分容積效應校正，稱為m-GTM，並與文獻中提到的其他常用演算法做比較。
m-GTM主要概念是將GTM方法中應用的校正區域縮小至影像像素大小，避免解剖影像對位與分割的需求，但由於待解的聯立方成組矩陣過於龐大，解值所需時間相當長且過程繁雜，於是運用簡化的方法，運算過程中只針對部分未知數求解，最後完成整組影像的校正。由結果可以觀察到，當系統解析度估測誤差為正負±8%範圍之內，mGTM方法較能恢復影像細節與強度值，特別是針對容易受到PVE的物體，其校正結果更優於其他校正方法的表現，且完成的影像也具有診斷方面的潛力。

Partial volume effect (PVE) is one of the major degradation effects for quantitation in PET due to finite system resolution and spatial sampling. To avoid quantiation bias casued by PVE in PET, correction for PVE is necessary but not routinely applied in clinical practice. There have been many different correction schemes proposed in the literature, including methods of deconvolution, and geometric transfer matrix (GTM). The popular and effective PVC method of geometric transfer matrix (GTM) was proposed by Rousset in 1998, and anatomic information (ex. MRI, CT) is needed in modeling PVE from different regions. Due to the requirement for anatomical images, segmentation and registration between PET and anatomical images are needed, and thus mis-segmentation and mis-registration would potentially introduce errors in the PVC results. In this thesis, a modified GTM method (mGTM) based on previous GTM algorithm was proposed, and the performance of the proposed mGTM was compared to other popular PVC methods from literatures. The major difference between mGTM and GTM is from region-based correction (GTM) to voxel-based processing (mGTM). Therefore, no anatomical information is required. Nevertheless, due to huge amount of data, the computation load for mGTM method is heavy. Thus the computational process in solving the original linear equations is simplfied by taking only a small set of variables each time. The results demonstrated that the proposed mGTM generated more accurate quantitation and better image recovery than other PVC methods and without any need for anatomical information. Future work will include more simulation and clinical data to verify the performance of mGTM method in 3D.

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