### Abstract

Traditionally, short scan helical FDK algorithms have been implemented based on horizontal transaxial slices. However, not every point on the horizontal transaxial slice satisfies Tuy's condition for the corresponding (pi + fan angle) segment of helix, which means that some points on the horizontal slices are incompletely sampled and are impossible to be exactly reconstructed. In this paper, we propose and implement an improved but still approximate short scan helical cone beam FDK algorithm based on nutating curved surfaces satisfying the Tuy's condition. This surface is defined by averaging PI surfaces emanating the initial and final source points of a (pi + fan angle) segment of helix. One of the key characteristics of the surface is that every point on it satisfies the Tuy's condition for the corresponding (pi + fan angle) segment of helix, which means that we can potentially reconstruct every point on the surface exactly. This difference makes the proposed algorithm deliver a better-reconstructed image quality while requiring a smaller detector area than that of traditional FDK methods based on horizontal transaxial slices. Another characteristic of the proposed surface is that every point within the helix belongs to one and only one such surface. Therefore, the location of the short scan segment for the reconstruction of a point in Cartesian coordinate could be precalculated and stored in a look-up table. This enables us to perform reconstruction directly on rectangular grids. We compare the performance of the improved FDK algorithm with that of a quasi-exact algorithm based on data combination technique. The simulation results show that the reconstructed image quality of these two methods is similar.

Original language | English (US) |
---|---|

Pages (from-to) | 1529-1536 |

Number of pages | 8 |

Journal | Medical Physics |

Volume | 32 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2005 |

### Keywords

- Cone beam
- Helical CT
- Image reconstruction
- Short scan

### ASJC Scopus subject areas

- Biophysics

### Cite this

*Medical Physics*,

*32*(6), 1529-1536. https://doi.org/10.1118/1.1916077

**An approximate short scan helical FDK cone beam algorithm based on nutating curved surfaces satisfying the Tuy's condition.** / Hu, Jicun; Tam, Kwok; Qi, Jinyi.

Research output: Contribution to journal › Article

*Medical Physics*, vol. 32, no. 6, pp. 1529-1536. https://doi.org/10.1118/1.1916077

}

TY - JOUR

T1 - An approximate short scan helical FDK cone beam algorithm based on nutating curved surfaces satisfying the Tuy's condition

AU - Hu, Jicun

AU - Tam, Kwok

AU - Qi, Jinyi

PY - 2005/6

Y1 - 2005/6

N2 - Traditionally, short scan helical FDK algorithms have been implemented based on horizontal transaxial slices. However, not every point on the horizontal transaxial slice satisfies Tuy's condition for the corresponding (pi + fan angle) segment of helix, which means that some points on the horizontal slices are incompletely sampled and are impossible to be exactly reconstructed. In this paper, we propose and implement an improved but still approximate short scan helical cone beam FDK algorithm based on nutating curved surfaces satisfying the Tuy's condition. This surface is defined by averaging PI surfaces emanating the initial and final source points of a (pi + fan angle) segment of helix. One of the key characteristics of the surface is that every point on it satisfies the Tuy's condition for the corresponding (pi + fan angle) segment of helix, which means that we can potentially reconstruct every point on the surface exactly. This difference makes the proposed algorithm deliver a better-reconstructed image quality while requiring a smaller detector area than that of traditional FDK methods based on horizontal transaxial slices. Another characteristic of the proposed surface is that every point within the helix belongs to one and only one such surface. Therefore, the location of the short scan segment for the reconstruction of a point in Cartesian coordinate could be precalculated and stored in a look-up table. This enables us to perform reconstruction directly on rectangular grids. We compare the performance of the improved FDK algorithm with that of a quasi-exact algorithm based on data combination technique. The simulation results show that the reconstructed image quality of these two methods is similar.

AB - Traditionally, short scan helical FDK algorithms have been implemented based on horizontal transaxial slices. However, not every point on the horizontal transaxial slice satisfies Tuy's condition for the corresponding (pi + fan angle) segment of helix, which means that some points on the horizontal slices are incompletely sampled and are impossible to be exactly reconstructed. In this paper, we propose and implement an improved but still approximate short scan helical cone beam FDK algorithm based on nutating curved surfaces satisfying the Tuy's condition. This surface is defined by averaging PI surfaces emanating the initial and final source points of a (pi + fan angle) segment of helix. One of the key characteristics of the surface is that every point on it satisfies the Tuy's condition for the corresponding (pi + fan angle) segment of helix, which means that we can potentially reconstruct every point on the surface exactly. This difference makes the proposed algorithm deliver a better-reconstructed image quality while requiring a smaller detector area than that of traditional FDK methods based on horizontal transaxial slices. Another characteristic of the proposed surface is that every point within the helix belongs to one and only one such surface. Therefore, the location of the short scan segment for the reconstruction of a point in Cartesian coordinate could be precalculated and stored in a look-up table. This enables us to perform reconstruction directly on rectangular grids. We compare the performance of the improved FDK algorithm with that of a quasi-exact algorithm based on data combination technique. The simulation results show that the reconstructed image quality of these two methods is similar.

KW - Cone beam

KW - Helical CT

KW - Image reconstruction

KW - Short scan

UR - http://www.scopus.com/inward/record.url?scp=21144453391&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21144453391&partnerID=8YFLogxK

U2 - 10.1118/1.1916077

DO - 10.1118/1.1916077

M3 - Article

C2 - 16013710

AN - SCOPUS:21144453391

VL - 32

SP - 1529

EP - 1536

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 6

ER -