### Abstract

Conventionally, the FDK algorithm is used to reconstruct images in many imaging systems where cone-beam projections are acquired from a single circular scanning path in a 2π angular range (full scan mode) and has been heuristically extended to a π+fan angle angular range (short-scan mode). In this paper, a new cone-beam reconstruction algorithm is derived for a single arc source trajectory with an equal weighting scheme. This algorithm is derived in the Katsevich framework. Since the single arc does not satisfy Tuy's data sufficiency condition, the resulting algorithm is an approximate reconstruction algorithm. The feature of one-dimensional (1D) shift-invariant filtering in the conventional FDK algorithm is nicely preserved. The new algorithm includes a voxel dependent backprojection step of weighted combinations of 1D Hilbert filtered data, after an initial differentiation operation. In comparing the new algorithm with the standard FDK: the new algorithm intrinsically handles full scan, short scan and super-short scan modes. Numerical simulations have been performed to validate the algorithm, and demonstrate more quantitatively correct density values when reconstructing points away from the central slice. Noise performance was assessed for both the new algorithm and the FDK algorithm using simulated Poisson noise.

Original language | English (US) |
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Pages (from-to) | 19-48 |

Number of pages | 30 |

Journal | Journal of X-Ray Science and Technology |

Volume | 15 |

Issue number | 1 |

State | Published - Mar 29 2007 |

### Keywords

- Approximate
- Circular trajectory
- Cone-beam
- FDK
- Reconstruction
- Shift-invariance

### ASJC Scopus subject areas

- Radiation
- Instrumentation
- Radiology Nuclear Medicine and imaging
- Condensed Matter Physics
- Electrical and Electronic Engineering

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## Cite this

*Journal of X-Ray Science and Technology*,

*15*(1), 19-48.