Making Binary Decisions Based on the Posterior Probability Distribution Associated with Tomographic Reconstructions

An optimal solution to the problem of making binary decisions about a local region of a reconstruction is provided by the Bayesian method. Decisions are made on the basis of the ratio of the posterior probabilities for the two alternative hypotheses. The full Bayesian procedure requires an integration of each posterior probability over all possible values of the image outside the local region being analyzed. In the present work, this full treatment is approximated by using the maximum value of the posterior probability obtained when the exterior region is varied with the interior fixed at each hypothesized functional form. A Monte Carlo procedure is employed to evaluate the benefit of this technique in a noisy four-view tomographic reconstruction situation for a detection task in which the signal is assumed to be exactly within a local region.

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