# The maximum likelihood estimator method of image reconstruction: Its fundamental characteristics and their origin

## Abstract

We review our recent work characterizing the image reconstruction properties of the MLE algorithm. We studied its convergence properties and confirmed the onset of image deterioration, which is a function of the number of counts in the source. By modulating the weight given to projection tubes with high numbers of counts with respect to those with low numbers of counts in the reconstruction process, we have confirmed that image deterioration is due to an attempt by the algorithm to match projection data tubes with high numbers of counts too closely to the iterative image projections. We developed a stopping rule for the algorithm that tests the hypothesis that a reconstructed image could have given the initial projection data in a manner consistent with the underlying assumption of Poisson distributed variables. The rule was applied to two mathematically generated phantoms with success and to a third phantom with exact (no statistical fluctuations) projection data. We conclude that the behavior of the target functions whose extrema are sought in iterative schemes is more important in the early stages of the reconstruction than in the later stages, when the extrema are being approached but with the Poisson nature of the measurement. 11 refs.,more »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley Lab., CA (USA)

- OSTI Identifier:
- 5933627

- Report Number(s):
- LBL-22417; CONF-8706213-1

ON: DE88000462

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Conference

- Resource Relation:
- Conference: 10. information processing in medical imaging international conference, Utrecht, Netherlands, 22 Jun 1987; Other Information: Portions of this document are illegible in microfiche products

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTANT EFFECTS ON LIVING ORGS. AND BIOL. MAT.; COMPUTERIZED TOMOGRAPHY; IMAGE PROCESSING; MAXIMUM-LIKELIHOOD FIT; ALGORITHMS; ITERATIVE METHODS; PHANTOMS; POISSON EQUATION; POSITRON COMPUTED TOMOGRAPHY; DIAGNOSTIC TECHNIQUES; DIFFERENTIAL EQUATIONS; EMISSION COMPUTED TOMOGRAPHY; EQUATIONS; MATHEMATICAL LOGIC; MOCKUP; NUMERICAL SOLUTION; PARTIAL DIFFERENTIAL EQUATIONS; PROCESSING; STRUCTURAL MODELS; TOMOGRAPHY; 560161* - Radionuclide Effects, Kinetics, & Toxicology- Man

### Citation Formats

```
Llacer, J, and Veklerov, E.
```*The maximum likelihood estimator method of image reconstruction: Its fundamental characteristics and their origin*. United States: N. p., 1987.
Web.

```
Llacer, J, & Veklerov, E.
```*The maximum likelihood estimator method of image reconstruction: Its fundamental characteristics and their origin*. United States.

```
Llacer, J, and Veklerov, E. Fri .
"The maximum likelihood estimator method of image reconstruction: Its fundamental characteristics and their origin". United States. https://www.osti.gov/servlets/purl/5933627.
```

```
@article{osti_5933627,
```

title = {The maximum likelihood estimator method of image reconstruction: Its fundamental characteristics and their origin},

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

abstractNote = {We review our recent work characterizing the image reconstruction properties of the MLE algorithm. We studied its convergence properties and confirmed the onset of image deterioration, which is a function of the number of counts in the source. By modulating the weight given to projection tubes with high numbers of counts with respect to those with low numbers of counts in the reconstruction process, we have confirmed that image deterioration is due to an attempt by the algorithm to match projection data tubes with high numbers of counts too closely to the iterative image projections. We developed a stopping rule for the algorithm that tests the hypothesis that a reconstructed image could have given the initial projection data in a manner consistent with the underlying assumption of Poisson distributed variables. The rule was applied to two mathematically generated phantoms with success and to a third phantom with exact (no statistical fluctuations) projection data. We conclude that the behavior of the target functions whose extrema are sought in iterative schemes is more important in the early stages of the reconstruction than in the later stages, when the extrema are being approached but with the Poisson nature of the measurement. 11 refs., 14 figs.},

doi = {},

url = {https://www.osti.gov/biblio/5933627},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1987},

month = {5}

}