title: Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data.
abstract: In this paper, a new image reconstruction scheme is presented based on Tuy's cone-beam inversion scheme and its fan-beam counterpart. It is demonstrated that Tuy's inversion scheme may be used to derive a new framework for fanbeam and cone-beam image reconstruction. In this new framework, images are reconstructed via filtering the backprojection image of differentiated projection data. The new framework is mathematically exact and is applicable to a general source trajectory provided the Tuy data sufficiency condition is satisfied. By choosing a piece-wise constant function for one of the components in the factorized weighting function, the filtering kernel is one dimensional, viz. the filtering process is along a straight line. Thus, the derived image reconstruction algorithm is mathematically exact and efficient. In the cone-beam case, the derived reconstruction algorithm is applicable to a large class of source trajectories where the pi-lines or the generalized pi-lines exist. In addition, the new reconstruction scheme survives the super-short scan mode in both the fan-beam and cone-beam cases provided the data are not transversely truncated. Numerical simulations were conducted to validate the new reconstruction scheme for the fan-beam case.
authors.affiliation: Department of Medical Physics, University of Wisconsin-Madison, WI 53704, USA.
authors.forename: Tingliang
authors.initials: T
authors.lastname: Zhuang
authors.forename: Shuai
authors.initials: S
authors.lastname: Leng
authors.forename: Brian E
authors.initials: BE
authors.lastname: Nett
authors.forename: Guang-Hong
authors.initials: GH
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D001921:Brain / Q000000981:diagnostic imaging*; D003198:Computer Simulation; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods; D016247:Information Storage and Retrieval / Q000379:methods; D008954:Models, Biological; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D036542:Tomography, Spiral Computed / Q000379:methods*