Ye Yangbo, Yu Hengyong, Wang Ge
Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA.
Int J Biomed Imaging. 2007;2007:10693. doi: 10.1155/2007/10693.
Using the backprojection filtration (BPF) and filtered backprojection (FBP) approaches, respectively, we prove that with cone-beam CT the interior problem can be exactly solved by analytic continuation. The prior knowledge we assume is that a volume of interest (VOI) in an object to be reconstructed is known in a subregion of the VOI. Our derivations are based on the so-called generalized PI-segment (chord). The available projection onto convex set (POCS) algorithm and singular value decomposition (SVD) method can be applied to perform the exact interior reconstruction. These results have many implications in the CT field and can be extended to other tomographic modalities, such as SPECT/PET, MRI.
我们分别使用反投影滤波（BPF）和滤波反投影（FBP）方法，证明了对于锥束CT，内部问题可以通过解析延拓精确求解。我们假设的先验知识是，待重建物体中的感兴趣体积（VOI）在VOI的一个子区域内是已知的。我们的推导基于所谓的广义PI段（弦）。可用的凸集投影（POCS）算法和奇异值分解（SVD）方法可用于执行精确的内部重建。这些结果在CT领域有许多应用，并可扩展到其他断层成像模态，如SPECT/PET、MRI。
