# MLE 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 Tomography (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 the 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., Univ. of California, Berkeley, CA (US)

- OSTI Identifier:
- 7057004

- Report Number(s):
- CONF-871006-

Journal ID: CODEN: IETNA; TRN: 88-024829

- Resource Type:
- Conference

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

- Additional Journal Information:
- Journal Volume: 35:1; 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:
- 61 RADIATION PROTECTION AND DOSIMETRY; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; BRAIN; PHANTOMS; IMAGE PROCESSING; POSITRON COMPUTED TOMOGRAPHY; ALGORITHMS; CALCULATION METHODS; COINCIDENCE METHODS; COMPTON EFFECT; COMPUTERIZED SIMULATION; IMAGE SCANNERS; ITERATIVE METHODS; MATRICES; MAXIMUM-LIKELIHOOD FIT; MONTE CARLO METHOD; POISSON EQUATION; RADIATION DETECTORS; BASIC INTERACTIONS; BODY; CENTRAL NERVOUS SYSTEM; COMPUTERIZED TOMOGRAPHY; COUNTING TECHNIQUES; DIAGNOSTIC TECHNIQUES; DIFFERENTIAL EQUATIONS; ELASTIC SCATTERING; ELECTROMAGNETIC INTERACTIONS; EMISSION COMPUTED TOMOGRAPHY; EQUATIONS; INTERACTIONS; MATHEMATICAL LOGIC; MEASURING INSTRUMENTS; MOCKUP; NERVOUS SYSTEM; NUMERICAL SOLUTION; ORGANS; PARTIAL DIFFERENTIAL EQUATIONS; PROCESSING; SCATTERING; SIMULATION; STRUCTURAL MODELS; TOMOGRAPHY; 655003* - Medical Physics- Dosimetry; 440101 - Radiation Instrumentation- General Detectors or Monitors & Radiometric Instruments; 990230 - Mathematics & Mathematical Models- (1987-1989)

### Citation Formats

```
Veklerov, E, Llacer, J, and Hoffman, E J.
```*MLE reconstruction of a brain phantom using a Monte Carlo transition matrix and a statistical stopping rule*. United States: N. p., 1988.
Web.

```
Veklerov, E, Llacer, J, & Hoffman, E J.
```*MLE 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. Mon .
"MLE reconstruction of a brain phantom using a Monte Carlo transition matrix and a statistical stopping rule". United States.
```

```
@article{osti_7057004,
```

title = {MLE 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 Tomography (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 the 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 with computer-simulated Poisson data.},

doi = {},

url = {https://www.osti.gov/biblio/7057004},
journal = {IEEE Trans. Nucl. Sci.; (United States)},

number = ,

volume = 35:1,

place = {United States},

year = {1988},

month = {2}

}