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The stochastic nature of the measurements used for image reconstruction from projections has largely been ignored in the past. If taken into account, the stochastic nature has been used to calculate the performance of algorithms which were developed independent of probabilistic considerations. This paper utilizes the knowledge of the probability density function of the measurements from the outset, and derives a reconstruction scheme which is optimal in the maximum likelihood sense. This algorithm is shown to yield an image which is unbiased -- that is, on the average it equals the object being reconstructed -- and which has the minimum variance of any estimator using the same measurements. As such, when operated in a stochastic environment, it will perform better than any current reconstruction technique, where the performance measures are the bias and viariance.