# MLE (Maximum Likelihood Estimator) reconstruction of a brain phantom using a Monte Carlo transition matrix and a statistical stopping rule

## Abstract

In order to study properties of the Maximum Likelihood Estimator (MLE) algorithm for image reconstruction in Positron Emission Tomographyy (PET), the algorithm is applied to data obtained by the ECAT-III tomograph from a brain phantom. The procedure for subtracting accidental coincidences from the data stream generated by this physical phantom is such that he resultant data are not Poisson distributed. This makes the present investigation different from other investigations based on computer-simulated phantoms. It is shown that the MLE algorithm is robust enough to yield comparatively good images, especially when the phantom is in the periphery of the field of view, even though the underlying assumption of the algorithm is violated. Two transition matrices are utilized. The first uses geometric considerations only. The second is derived by a Monte Carlo simulation which takes into account Compton scattering in the detectors, positron range, etc. in the detectors. It is demonstrated that the images obtained from the Monte Carlo matrix are superior in some specific ways. A stopping rule derived earlier and allowing the user to stop the iterative process before the images begin to deteriorate is tested. Since the rule is based on the Poisson assumption, it does not work wellmore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley Lab., CA (USA); California Univ., Los Angeles (USA). Dept. of Radiological Sciences

- OSTI Identifier:
- 5205389

- Report Number(s):
- LBL-23357; CONF-871006-51

ON: DE88008219

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Conference

- Resource Relation:
- Conference: 34. nuclear science symposium and 19. nuclear power systems symposium, San Francisco, CA, USA, 21 Oct 1987

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 62 RADIOLOGY AND NUCLEAR MEDICINE; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; BRAIN; IMAGES; POSITRON COMPUTED TOMOGRAPHY; ALGORITHMS; COMPUTERIZED SIMULATION; IMAGE PROCESSING; MATRICES; MONTE CARLO METHOD; PHANTOMS; STATISTICS; BODY; CENTRAL NERVOUS SYSTEM; COMPUTERIZED TOMOGRAPHY; DIAGNOSTIC TECHNIQUES; EMISSION COMPUTED TOMOGRAPHY; MATHEMATICAL LOGIC; MATHEMATICS; MOCKUP; NERVOUS SYSTEM; ORGANS; PROCESSING; SIMULATION; STRUCTURAL MODELS; TOMOGRAPHY; 550602* - Medicine- External Radiation in Diagnostics- (1980-); 990220 - Computers, Computerized Models, & Computer Programs- (1987-1989)

### Citation Formats

```
Veklerov, E, Llacer, J, and Hoffman, E J.
```*MLE (Maximum Likelihood Estimator) reconstruction of a brain phantom using a Monte Carlo transition matrix and a statistical stopping rule*. United States: N. p., 1987.
Web.

```
Veklerov, E, Llacer, J, & Hoffman, E J.
```*MLE (Maximum Likelihood Estimator) reconstruction of a brain phantom using a Monte Carlo transition matrix and a statistical stopping rule*. United States.

```
Veklerov, E, Llacer, J, and Hoffman, E J. Thu .
"MLE (Maximum Likelihood Estimator) reconstruction of a brain phantom using a Monte Carlo transition matrix and a statistical stopping rule". United States. https://www.osti.gov/servlets/purl/5205389.
```

```
@article{osti_5205389,
```

title = {MLE (Maximum Likelihood Estimator) reconstruction of a brain phantom using a Monte Carlo transition matrix and a statistical stopping rule},

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

abstractNote = {In order to study properties of the Maximum Likelihood Estimator (MLE) algorithm for image reconstruction in Positron Emission Tomographyy (PET), the algorithm is applied to data obtained by the ECAT-III tomograph from a brain phantom. The procedure for subtracting accidental coincidences from the data stream generated by this physical phantom is such that he resultant data are not Poisson distributed. This makes the present investigation different from other investigations based on computer-simulated phantoms. It is shown that the MLE algorithm is robust enough to yield comparatively good images, especially when the phantom is in the periphery of the field of view, even though the underlying assumption of the algorithm is violated. Two transition matrices are utilized. The first uses geometric considerations only. The second is derived by a Monte Carlo simulation which takes into account Compton scattering in the detectors, positron range, etc. in the detectors. It is demonstrated that the images obtained from the Monte Carlo matrix are superior in some specific ways. A stopping rule derived earlier and allowing the user to stop the iterative process before the images begin to deteriorate is tested. Since the rule is based on the Poisson assumption, it does not work well with the presently available data, although it is successful wit computer-simulated Poisson data.},

doi = {},

url = {https://www.osti.gov/biblio/5205389},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1987},

month = {10}

}