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

Conference · Fri May 01 04:00:00 EDT 1987

OSTI ID:5933627

Llacer, J; Veklerov, E

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.

• Research Organization: Lawrence Berkeley Lab., CA (USA)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5933627
• Report Number(s): LBL-22417; CONF-8706213-1; ON: DE88000462
• Country of Publication: United States
• Language: English

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