Department of Biomedical Engineering, School of Life Science & Technology, Beijing Institute of Technology, Beijing 100081, People's Republic of China.
Phys Med Biol. 2010 Mar 21;55(6):1631-41. doi: 10.1088/0031-9155/55/6/007. Epub 2010 Feb 24.
Due to its simplicity, parallel-beam geometry is usually assumed for the development of image reconstruction algorithms. The established reconstruction methodologies are then extended to fan-beam, cone-beam and other non-parallel geometries for practical application. This situation occurs for quantitative SPECT (single photon emission computed tomography) imaging in inverting the attenuated Radon transform. Novikov reported an explicit parallel-beam formula for the inversion of the attenuated Radon transform in 2000. Thereafter, a formula for fan-beam geometry was reported by Bukhgeim and Kazantsev (2002 Preprint N. 99 Sobolev Institute of Mathematics). At the same time, we presented a formula for varying focal-length fan-beam geometry. Sometimes, the reconstruction formula is so implicit that we cannot obtain the explicit reconstruction formula in the non-parallel geometries. In this work, we propose a unified reconstruction framework for extending parallel-beam geometry to any non-parallel geometry using ray-driven techniques. Studies by computer simulations demonstrated the accuracy of the presented unified reconstruction framework for extending parallel-beam to non-parallel geometries in inverting the attenuated Radon transform.
由于其简单性，通常假设用于开发图像重建算法的是平行束几何形状。然后，将既定的重建方法扩展到扇束、锥束和其他非平行几何形状，以进行实际应用。这种情况发生在定量单光子发射计算机断层扫描（SPECT）成像中，用于反演衰减的 Radon 变换。Novikov 在 2000 年报告了用于反演衰减的 Radon 变换的显式平行束公式。此后，Bukhgeim 和 Kazantsev（2002 年预印本 N. 99 Sobolev 数学研究所）报告了扇束几何形状的公式。同时，我们提出了一个用于变化焦距扇束几何形状的公式。有时，重建公式是如此隐含，以至于我们无法在非平行几何形状中获得显式重建公式。在这项工作中，我们提出了一个统一的重建框架，用于使用射线驱动技术将平行束几何形状扩展到任何非平行几何形状。计算机模拟研究表明，所提出的用于将平行束扩展到非平行几何形状的统一重建框架在反演衰减的 Radon 变换中用于扩展平行束的准确性。
