### Abstract

Performing image reconstruction from cone-beam projections is required for both X-ray computed tomography (CT) and single photon emission computed tomography (SPECT). The Grangeat's algorithm consists of three stages: 1) obtaining the first derivative of the plane integral (3D Radon transform) from cone-beam projections, 2) rebinning the data and calculating the second derivative, and 3) reconstructing the image using the 3D Radon backprojection. Recently, a new implementation method of Grangeat's algorithm for the 1st stage using spherical harmonics, has been proposed for the short-object problem with a huge-detector [1- 2]. We have modified the method using spherical harmonics to solve the short-object problem with a midsize-detector. The 1st stage can be described by the following three steps: 1a) masking the cone-beam projections at each cone vertex position, 1b) calculating partial data of the 1st derivative of the 3D Radon transform from masked data using spherical harmonics (similar to [1-2]), and 1c) obtaining complete data of the 1st derivative of the 3D Radon transform using the partial data at plural cone vertex positions. If the trajectory of the cone vertex satisfies Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction. Computer simulations were performed to verify the approach.

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

Editors | D. Merelli, J. Surget, M. Ulma |

Volume | 2 |

State | Published - 2000 |

Externally published | Yes |

Event | 2000 IEEE Nuclear Science Symposium Conference Record - Lyon, France Duration: Oct 15 2000 → Oct 20 2000 |

### Other

Other | 2000 IEEE Nuclear Science Symposium Conference Record |
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Country | France |

City | Lyon |

Period | 10/15/00 → 10/20/00 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Vision and Pattern Recognition
- Industrial and Manufacturing Engineering

### Cite this

*IEEE Nuclear Science Symposium and Medical Imaging Conference*(Vol. 2)

**Cone-beam image reconstruction using spherical harmonics : Short-object problem with midsize-detector.** / Taguchi, Katsuyuki; Zeng, Gengsheng L.; Gullberg, Grant T.

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

*IEEE Nuclear Science Symposium and Medical Imaging Conference.*vol. 2, 2000 IEEE Nuclear Science Symposium Conference Record, Lyon, France, 10/15/00.

}

TY - GEN

T1 - Cone-beam image reconstruction using spherical harmonics

T2 - Short-object problem with midsize-detector

AU - Taguchi, Katsuyuki

AU - Zeng, Gengsheng L.

AU - Gullberg, Grant T.

PY - 2000

Y1 - 2000

N2 - Performing image reconstruction from cone-beam projections is required for both X-ray computed tomography (CT) and single photon emission computed tomography (SPECT). The Grangeat's algorithm consists of three stages: 1) obtaining the first derivative of the plane integral (3D Radon transform) from cone-beam projections, 2) rebinning the data and calculating the second derivative, and 3) reconstructing the image using the 3D Radon backprojection. Recently, a new implementation method of Grangeat's algorithm for the 1st stage using spherical harmonics, has been proposed for the short-object problem with a huge-detector [1- 2]. We have modified the method using spherical harmonics to solve the short-object problem with a midsize-detector. The 1st stage can be described by the following three steps: 1a) masking the cone-beam projections at each cone vertex position, 1b) calculating partial data of the 1st derivative of the 3D Radon transform from masked data using spherical harmonics (similar to [1-2]), and 1c) obtaining complete data of the 1st derivative of the 3D Radon transform using the partial data at plural cone vertex positions. If the trajectory of the cone vertex satisfies Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction. Computer simulations were performed to verify the approach.

AB - Performing image reconstruction from cone-beam projections is required for both X-ray computed tomography (CT) and single photon emission computed tomography (SPECT). The Grangeat's algorithm consists of three stages: 1) obtaining the first derivative of the plane integral (3D Radon transform) from cone-beam projections, 2) rebinning the data and calculating the second derivative, and 3) reconstructing the image using the 3D Radon backprojection. Recently, a new implementation method of Grangeat's algorithm for the 1st stage using spherical harmonics, has been proposed for the short-object problem with a huge-detector [1- 2]. We have modified the method using spherical harmonics to solve the short-object problem with a midsize-detector. The 1st stage can be described by the following three steps: 1a) masking the cone-beam projections at each cone vertex position, 1b) calculating partial data of the 1st derivative of the 3D Radon transform from masked data using spherical harmonics (similar to [1-2]), and 1c) obtaining complete data of the 1st derivative of the 3D Radon transform using the partial data at plural cone vertex positions. If the trajectory of the cone vertex satisfies Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction. Computer simulations were performed to verify the approach.

UR - http://www.scopus.com/inward/record.url?scp=0034593663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034593663&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0034593663

VL - 2

BT - IEEE Nuclear Science Symposium and Medical Imaging Conference

A2 - Merelli, D.

A2 - Surget, J.

A2 - Ulma, M.

ER -