# Towards a practical implementation of the MLE algorithm for positron emission tomography

## Abstract

Recognizing that the quality of images obtained by application of the Maximum Likelihood Estimator (MLE) to Positron Emission Tomography (PET) and Single Photon Emission Tomography (SPECT) appears to be substantially better than those obtained by conventional methods, the authors have started to develop methods that will facilitate the necessary research for a good evaluation of the algorithm and may lead to its practical application for research and routine tomography. They have found that the non-linear MLE algorithm can be used with pixel sizes which are smaller than the sampling distance, without interpolation, obtaining excellent resolution and no noticeable increase in noise. They have studied the role of symmetry in reducing the amount of matrix element storage requirements for full size applications of the algorithm and have used that concept to carry out two reconstructions of the Derenzo phantom with data from the ECAT-III instrument. The results show excellent signal-to-noise (S/N) ratio, particularly for data with low total counts, excellent sharpness, but low contrast at high frequencies when using the Shepp-Vardi model for probability matrices.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley Lab., Univ. of California, Berkeley, CA 94720

- OSTI Identifier:
- 5943232

- Report Number(s):
- CONF-851009-

Journal ID: CODEN: IETNA; TRN: 86-013632

- Resource Type:
- Conference

- Journal Name:
- IEEE Trans. Nucl. Sci.; (United States)

- Additional Journal Information:
- Journal Volume: NS-33:1; Conference: IEEE nuclear science symposium, San Francisco, CA, USA, 23 Oct 1985

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 62 RADIOLOGY AND NUCLEAR MEDICINE; POSITRON COMPUTED TOMOGRAPHY; ALGORITHMS; SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY; ECAT SCANNING; FREQUENCY DEPENDENCE; MATHEMATICAL MODELS; MATRICES; MAXIMUM-LIKELIHOOD FIT; MEMORY DEVICES; NONLINEAR PROBLEMS; PROBABILITY; RESEARCH PROGRAMS; SIGNAL-TO-NOISE RATIO; SYMMETRY; COMPUTERIZED TOMOGRAPHY; DIAGNOSTIC TECHNIQUES; EMISSION COMPUTED TOMOGRAPHY; MATHEMATICAL LOGIC; NUMERICAL SOLUTION; PHOTON EMISSION SCANNING; TOMOGRAPHY; 550602* - Medicine- External Radiation in Diagnostics- (1980-)

### Citation Formats

```
Llacer, J, Andreae, S, Veklerov, E, and Hoffman, E J.
```*Towards a practical implementation of the MLE algorithm for positron emission tomography*. United States: N. p., 1986.
Web.

```
Llacer, J, Andreae, S, Veklerov, E, & Hoffman, E J.
```*Towards a practical implementation of the MLE algorithm for positron emission tomography*. United States.

```
Llacer, J, Andreae, S, Veklerov, E, and Hoffman, E J. Sat .
"Towards a practical implementation of the MLE algorithm for positron emission tomography". United States.
```

```
@article{osti_5943232,
```

title = {Towards a practical implementation of the MLE algorithm for positron emission tomography},

author = {Llacer, J and Andreae, S and Veklerov, E and Hoffman, E J},

abstractNote = {Recognizing that the quality of images obtained by application of the Maximum Likelihood Estimator (MLE) to Positron Emission Tomography (PET) and Single Photon Emission Tomography (SPECT) appears to be substantially better than those obtained by conventional methods, the authors have started to develop methods that will facilitate the necessary research for a good evaluation of the algorithm and may lead to its practical application for research and routine tomography. They have found that the non-linear MLE algorithm can be used with pixel sizes which are smaller than the sampling distance, without interpolation, obtaining excellent resolution and no noticeable increase in noise. They have studied the role of symmetry in reducing the amount of matrix element storage requirements for full size applications of the algorithm and have used that concept to carry out two reconstructions of the Derenzo phantom with data from the ECAT-III instrument. The results show excellent signal-to-noise (S/N) ratio, particularly for data with low total counts, excellent sharpness, but low contrast at high frequencies when using the Shepp-Vardi model for probability matrices.},

doi = {},

url = {https://www.osti.gov/biblio/5943232},
journal = {IEEE Trans. Nucl. Sci.; (United States)},

number = ,

volume = NS-33:1,

place = {United States},

year = {1986},

month = {2}

}