### Abstract

FDK method is the most popular cone beam algorithm to date. 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 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 characteristics of the proposed surface is that every point in the object space belongs to one and only one such surface. Therefore, the location of the short scan segment for reconstruction of a point in Cartesian coordinate can be pre-calculated 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 about the same. We also provide a qualitative analysis of the link between the improved FDK and exact methods. The computational requirement of the proposed algorithm is the same as that of the traditional FDK method. We validate the proposed algorithm with a disc phantom.

Original language | English (US) |
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Title of host publication | IEEE Nuclear Science Symposium Conference Record |

Editors | J.A. Seibert |

Pages | 2760-2764 |

Number of pages | 5 |

Volume | 5 |

State | Published - 2004 |

Event | 2004 Nuclear Science Symposium, Medical Imaging Conference, Symposium on Nuclear Power Systems and the 14th International Workshop on Room Temperature Semiconductor X- and Gamma- Ray Detectors - Rome, Italy Duration: Oct 16 2004 → Oct 22 2004 |

### Other

Other | 2004 Nuclear Science Symposium, Medical Imaging Conference, Symposium on Nuclear Power Systems and the 14th International Workshop on Room Temperature Semiconductor X- and Gamma- Ray Detectors |
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Country | Italy |

City | Rome |

Period | 10/16/04 → 10/22/04 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Vision and Pattern Recognition
- Industrial and Manufacturing Engineering

### Cite this

*IEEE Nuclear Science Symposium Conference Record*(Vol. 5, pp. 2760-2764). [M2-453]

**A short scan helical FDK cone beam algorithm based on surfaces satisfying the Tuy's condition.** / Hu, Jicun; Tam, Kwok; Johnson, Roger H.; Qi, Jinyi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE Nuclear Science Symposium Conference Record.*vol. 5, M2-453, pp. 2760-2764, 2004 Nuclear Science Symposium, Medical Imaging Conference, Symposium on Nuclear Power Systems and the 14th International Workshop on Room Temperature Semiconductor X- and Gamma- Ray Detectors, Rome, Italy, 10/16/04.

}

TY - GEN

T1 - A short scan helical FDK cone beam algorithm based on surfaces satisfying the Tuy's condition

AU - Hu, Jicun

AU - Tam, Kwok

AU - Johnson, Roger H.

AU - Qi, Jinyi

PY - 2004

Y1 - 2004

N2 - FDK method is the most popular cone beam algorithm to date. 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 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 characteristics of the proposed surface is that every point in the object space belongs to one and only one such surface. Therefore, the location of the short scan segment for reconstruction of a point in Cartesian coordinate can be pre-calculated 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 about the same. We also provide a qualitative analysis of the link between the improved FDK and exact methods. The computational requirement of the proposed algorithm is the same as that of the traditional FDK method. We validate the proposed algorithm with a disc phantom.

AB - FDK method is the most popular cone beam algorithm to date. 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 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 characteristics of the proposed surface is that every point in the object space belongs to one and only one such surface. Therefore, the location of the short scan segment for reconstruction of a point in Cartesian coordinate can be pre-calculated 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 about the same. We also provide a qualitative analysis of the link between the improved FDK and exact methods. The computational requirement of the proposed algorithm is the same as that of the traditional FDK method. We validate the proposed algorithm with a disc phantom.

UR - http://www.scopus.com/inward/record.url?scp=23844518539&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23844518539&partnerID=8YFLogxK

M3 - Conference contribution

VL - 5

SP - 2760

EP - 2764

BT - IEEE Nuclear Science Symposium Conference Record

A2 - Seibert, J.A.

ER -