title: A general exact method for synthesizing parallel-beam projections from cone-beam projections via filtered backprojection.
abstract: In recent years, image reconstruction methods for cone-beam computed tomography (CT) have been extensively studied. However, few of these studies discussed computing parallel-beam projections from cone-beam projections. In this paper, we focus on the exact synthesis of complete or incomplete parallel-beam projections from cone-beam projections. First, an extended central slice theorem is described to establish a relationship between the Radon space and the Fourier space. Then, data sufficiency conditions are proposed for computing parallel-beam projection data from cone-beam data. Using these results, a general filtered backprojection algorithm is formulated that can exactly synthesize parallel-beam projection data from cone-beam projection data. As an example, we prove that parallel-beam projections can be exactly synthesized in an angular range in the case of circular cone-beam scanning. Interestingly, this angular range is larger than that derived in the Feldkamp reconstruction framework. Numerical experiments are performed in the circular scanning case to verify our method.
authors.affiliation: Department of Engineering Physics, Tsinghua University, Beijing 100084, People's Republic of China. liliang02@mails.tsinghua.edu.cn
authors.forename: Liang
authors.initials: L
authors.lastname: Li
authors.forename: Zhiqiang
authors.initials: Z
authors.lastname: Chen
authors.forename: Yuxiang
authors.initials: Y
authors.lastname: Xing
authors.forename: Li
authors.initials: L
authors.lastname: Zhang
authors.forename: Kejun
authors.initials: K
authors.lastname: Kang
authors.forename: Ge
authors.initials: G
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D016477:Artifacts; D003198:Computer Simulation; D005583:Fourier Analysis; D007091:Image Processing, Computer-Assisted / Q000379:methods; D015233:Models, Statistical; D008962:Models, Theoretical; D012542:Scattering, Radiation; D012984:Software; D036542:Tomography, Spiral Computed / Q000379:methods*; D014057:Tomography, X-Ray Computed / Q000379:methods*