Currently used methods of computerized tomographic image reconstruction require a large number of measurements relative to the number of picture elements to be estimated, but employ computationally simple algorithms. However these reconstruction methods do not optimally use the information contained in the measurements. Using a stochastic analysis, the inherent statistical assumptions of some seemingly deterministic reconstruction techniques are examined, and a class of recursive algorithms are developed which use data more efficiently at the price of a small increase in computational complexity per measurement. These algorithms will be useful in cases where the number of measurements are limited by time, cost, geometry, or independence constraints. Examples of reconstructions using state-estimation methods such as square-root, Chandrasekhar, and related algorithms will be discussed.