# Propagation of errors from the sensitivity image in list mode reconstruction

## 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.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Director, Office of Science. Office of Biological and Environmental Research. Medical Sciences Division; National Institutes of Health (US)

- OSTI Identifier:
- 820667

- Report Number(s):
- LBNL-54082

R&D Project: 865A1A; TRN: US0400372

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Conference

- Resource Relation:
- Conference: IEEE Nuclear Science Symposium and Medical Imaging Conference, Portland, OR (US), 10/21/2003--10/25/2003; Other Information: PBD: 15 Nov 2003

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 62 RADIOLOGY AND NUCLEAR MEDICINE; ATTENUATION; COMPUTERIZED SIMULATION; DETECTION; EFFICIENCY; SENSITIVITY; STORAGE

### Citation Formats

```
Qi, Jinyi, and Huesman, Ronald H.
```*Propagation of errors from the sensitivity image in list mode reconstruction*. United States: N. p., 2003.
Web.

```
Qi, Jinyi, & Huesman, Ronald H.
```*Propagation of errors from the sensitivity image in list mode reconstruction*. United States.

```
Qi, Jinyi, and Huesman, Ronald H. Sat .
"Propagation of errors from the sensitivity image in list mode reconstruction". United States. https://www.osti.gov/servlets/purl/820667.
```

```
@article{osti_820667,
```

title = {Propagation of errors from the sensitivity image in list mode reconstruction},

author = {Qi, Jinyi and Huesman, Ronald H.},

abstractNote = {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.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2003},

month = {11}

}