### 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) |
---|---|

Pages (from-to) | 19-48 |

Number of pages | 30 |

Journal | Journal of X-Ray Science and Technology |

Volume | 15 |

Issue number | 1 |

State | Published - 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Radiology Nuclear Medicine and imaging

### Cite this

*Journal of X-Ray Science and Technology*,

*15*(1), 19-48.

**Arc based cone-beam reconstruction algorithm using an equal weighting scheme.** / Nett, Brian E.; Zhuang, Ting Liang; Leng, Shuai; Chen, Guang Hong.

Research output: Contribution to journal › Article

*Journal of X-Ray Science and Technology*, vol. 15, no. 1, pp. 19-48.

}

TY - JOUR

T1 - Arc based cone-beam reconstruction algorithm using an equal weighting scheme

AU - Nett, Brian E.

AU - Zhuang, Ting Liang

AU - Leng, Shuai

AU - Chen, Guang Hong

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Approximate

KW - Circular trajectory

KW - Cone-beam

KW - FDK

KW - Reconstruction

KW - Shift-invariance

UR - http://www.scopus.com/inward/record.url?scp=33947492818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947492818&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33947492818

VL - 15

SP - 19

EP - 48

JO - Journal of X-Ray Science and Technology

JF - Journal of X-Ray Science and Technology

SN - 0895-3996

IS - 1

ER -