title: A SPECT reconstruction method for extending parallel to non-parallel geometries.
abstract: 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.
authors.affiliation: Department of Biomedical Engineering, School of Life Science & Technology, Beijing Institute of Technology, Beijing 100081, People's Republic of China. wenjh@bit.edu.cn
authors.forename: Junhai
authors.initials: J
authors.lastname: Wen
authors.forename: Zhengrong
authors.initials: Z
authors.lastname: Liang
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D011886:Radon; D012680:Sensitivity and Specificity; D015899:Tomography, Emission-Computed, Single-Photon / Q000379:methods*
chemical_list: D011886:Radon