A general exact method for synthesizing parallel-beam projections from cone-beam projections via filtered backprojection.
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.
Li
Liang
L
Department of Engineering Physics, Tsinghua University, Beijing 100084, People's Republic of China. liliang02@mails.tsinghua.edu.cn
Chen
Zhiqiang
Z
Xing
Yuxiang
Y
Zhang
Li
L
Kang
Kejun
K
Wang
Ge
G
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*