Yu Hengyong, Yang Jiansheng, Jiang Ming, Wang Ge
CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engineering Virginia Tech, Blacksburg, VA 24061, USA.
Commun Numer Methods Eng. 2009 Jun 1;25(6):693-710. doi: 10.1002/cnm.1206.
Single photon emission computed tomography (SPECT) is an important biomedical imaging modality. However, since gamma cameras are expensive and bulky, truncated projection data are either preferred or unavoidable. Inspired by the recent results on interior tomography in the x-ray CT field, here we present the interior SPECT approach for exact and stable reconstruction of a region of interest (ROI) from uniformly attenuated local projection data, aided by prior knowledge of a sub-region in the ROI. First, by analytic continuation we prove that interior SPECT is both exact and stable, and by singular value decomposition (SVD) we establish the stability of interior SPECT. Then, given the constant attenuation coefficient and object boundary, our interior SPECT reconstruction is achieved by inverting a generalized truncated Hilbert transform using the SVD technique. Preliminary numerical simulation data demonstrate that our work has practical utilities. The theoretical generalization of our work to the variable attenuation case is underway, and the same numerical approach can be applied.
单光子发射计算机断层扫描（SPECT）是一种重要的生物医学成像模态。然而，由于伽马相机昂贵且体积庞大，截断投影数据要么是首选的，要么是不可避免的。受X射线CT领域内断层扫描近期成果的启发，在此我们提出一种内部SPECT方法，用于从均匀衰减的局部投影数据中精确且稳定地重建感兴趣区域（ROI），并借助ROI中一个子区域的先验知识。首先，通过解析延拓我们证明内部SPECT既精确又稳定，并且通过奇异值分解（SVD）我们建立了内部SPECT的稳定性。然后，给定恒定的衰减系数和物体边界，我们的内部SPECT重建通过使用SVD技术对广义截断希尔伯特变换求逆来实现。初步的数值模拟数据表明我们的工作具有实际效用。我们工作对可变衰减情况的理论推广正在进行中，并且可以应用相同的数值方法。
