### Abstract

List mode image reconstruction is attracting renewed attention. It eliminates the storage of empty sinogram bins. However, a single back projection of all LORs is still necessary for the pre-calculation of a sensitivity image. Since the detection sensitivity is dependent on the object attenuation and detector efficiency, it must be computed for each study. Exact computation of the sensitivity image can be a daunting task for modern scanners with huge numbers of LORs. Thus, some fast approximate calculation may be desirable. In this paper, we theoretically analyze the error propagation from the sensitivity image into the reconstructed image. The theoretical analysis is based on the fixed point condition of the list mode reconstruction. The non-negativity constraint is modeled using the Kuhn-Tucker condition. With certain assumptions and the first order Taylor series approximation, we derive a closed form expression for the error in the reconstructed image as a function of the error in the sensitivity image. The result provides insights on what kind of error might be allowable in the sensitivity image. Computer simulations show that the theoretical results are in good agreement with the measured results.

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

Editors | S.D. Metzler |

Pages | 3087-3091 |

Number of pages | 5 |

Volume | 5 |

State | Published - 2003 |

Externally published | Yes |

Event | 2003 IEEE Nuclear Science Symposium Conference Record - Nuclear Science Symposium, Medical Imaging Conference - Portland, OR, United States Duration: Oct 19 2003 → Oct 25 2003 |

### Other

Other | 2003 IEEE Nuclear Science Symposium Conference Record - Nuclear Science Symposium, Medical Imaging Conference |
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Country | United States |

City | Portland, OR |

Period | 10/19/03 → 10/25/03 |

### 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. 3087-3091). [M14-222]

**Propagation of errors from the sensitivity image in list mode reconstruction.** / Qi, Jinyi; Huesman, Ronald H.

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

*IEEE Nuclear Science Symposium Conference Record.*vol. 5, M14-222, pp. 3087-3091, 2003 IEEE Nuclear Science Symposium Conference Record - Nuclear Science Symposium, Medical Imaging Conference, Portland, OR, United States, 10/19/03.

}

TY - GEN

T1 - Propagation of errors from the sensitivity image in list mode reconstruction

AU - Qi, Jinyi

AU - Huesman, Ronald H.

PY - 2003

Y1 - 2003

N2 - List mode image reconstruction is attracting renewed attention. It eliminates the storage of empty sinogram bins. However, a single back projection of all LORs is still necessary for the pre-calculation of a sensitivity image. Since the detection sensitivity is dependent on the object attenuation and detector efficiency, it must be computed for each study. Exact computation of the sensitivity image can be a daunting task for modern scanners with huge numbers of LORs. Thus, some fast approximate calculation may be desirable. In this paper, we theoretically analyze the error propagation from the sensitivity image into the reconstructed image. The theoretical analysis is based on the fixed point condition of the list mode reconstruction. The non-negativity constraint is modeled using the Kuhn-Tucker condition. With certain assumptions and the first order Taylor series approximation, we derive a closed form expression for the error in the reconstructed image as a function of the error in the sensitivity image. The result provides insights on what kind of error might be allowable in the sensitivity image. Computer simulations show that the theoretical results are in good agreement with the measured results.

AB - List mode image reconstruction is attracting renewed attention. It eliminates the storage of empty sinogram bins. However, a single back projection of all LORs is still necessary for the pre-calculation of a sensitivity image. Since the detection sensitivity is dependent on the object attenuation and detector efficiency, it must be computed for each study. Exact computation of the sensitivity image can be a daunting task for modern scanners with huge numbers of LORs. Thus, some fast approximate calculation may be desirable. In this paper, we theoretically analyze the error propagation from the sensitivity image into the reconstructed image. The theoretical analysis is based on the fixed point condition of the list mode reconstruction. The non-negativity constraint is modeled using the Kuhn-Tucker condition. With certain assumptions and the first order Taylor series approximation, we derive a closed form expression for the error in the reconstructed image as a function of the error in the sensitivity image. The result provides insights on what kind of error might be allowable in the sensitivity image. Computer simulations show that the theoretical results are in good agreement with the measured results.

UR - http://www.scopus.com/inward/record.url?scp=11944252391&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11944252391&partnerID=8YFLogxK

M3 - Conference contribution

VL - 5

SP - 3087

EP - 3091

BT - IEEE Nuclear Science Symposium Conference Record

A2 - Metzler, S.D.

ER -