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 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 nonnegativity 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 shows that the error response is frequency-dependent and provides a simple expression for determining the required accuracy of the sensitivity image calculation. Computer simulations show that the theoretical results are in good agreement with the measured results.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1094-1099 |
| Number of pages | 6 |
| Journal | IEEE Transactions on Medical Imaging |
| Volume | 23 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 2004 |
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Keywords
- Emission tomography
- Error propagation
- List mode reconstruction
- Poisson likelihood
- Sensitivity image
ASJC Scopus subject areas
- Biomedical Engineering
- Radiology Nuclear Medicine and imaging
- Radiological and Ultrasound Technology
- Electrical and Electronic Engineering
- Computer Science Applications
- Computational Theory and Mathematics
Cite this
Propagation of errors from the sensitivity image in list mode reconstruction. / Qi, Jinyi; Huesman, Ronald H.
In: IEEE Transactions on Medical Imaging, Vol. 23, No. 9, 09.2004, p. 1094-1099.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Propagation of errors from the sensitivity image in list mode reconstruction
AU - Qi, Jinyi
AU - Huesman, Ronald H.
PY - 2004/9
Y1 - 2004/9
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 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 nonnegativity 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 shows that the error response is frequency-dependent and provides a simple expression for determining the required accuracy of the sensitivity image calculation. 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 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 nonnegativity 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 shows that the error response is frequency-dependent and provides a simple expression for determining the required accuracy of the sensitivity image calculation. Computer simulations show that the theoretical results are in good agreement with the measured results.
KW - Emission tomography
KW - Error propagation
KW - List mode reconstruction
KW - Poisson likelihood
KW - Sensitivity image
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UR - http://www.scopus.com/inward/citedby.url?scp=4444299712&partnerID=8YFLogxK
U2 - 10.1109/TMI.2004.829333
DO - 10.1109/TMI.2004.829333
M3 - Article
C2 - 15377118
AN - SCOPUS:4444299712
VL - 23
SP - 1094
EP - 1099
JO - IEEE Transactions on Medical Imaging
JF - IEEE Transactions on Medical Imaging
SN - 0278-0062
IS - 9
ER -