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A new statistical reconstruction method based on origin ensembles (OE) for emission tomography (ET) is examined. Using a probability density function (pdf) derived from first principles, an ensemble expectation of numbers of detected event origins per voxel is determined. These numbers divided by sensitivities of voxels and acquisition time provide OE estimates of the voxel activities. The OE expectations are shown to be the same as expectations calculated using the complete-data space. The properties of the OE estimate are examined. It is shown that OE estimate approximates maximum likelihood (ML) estimate for conditions usually achieved in practical applications in emission tomography. Three numerical experiments with increasing complexity are used to validate theoretical findings and demonstrate similarities of ML and OE estimates. Recommendations for achieving improved accuracy and speed of OE reconstructions are provided.