Conditional event algebra techniques for iterated image estimation

Practical sequential estimation algorithms inherently involve ''iterated conditioning''; that is, the estimate at any algorithm step is conditioned on information passed from the previous step. Except in special cases, standard probability theory cannot deal with operations like iterated conditioning, so it is difficult even to formulate algorithms that make optimal use of the available information. The recently developed Product Space Conditional Event Algebra (PS-CEA) allows for the definition of ''conditional events'' as regular events in a probability space, and thus for the extension of Bayesian analysis to cases of iterated conditioning. In this paper, we describe the PS-CEA approach and give an example of its use in deriving iterated image estimators when the information passed from one stage to the next is the current image estimate.