*Maximum Entropy and Bayesian Methods*, pp. 313-326 (Kluwer Academic, Dordrecht, 1991)

## Making binary decisions based on the posterior probability distribution associated with tomographic reconstructions

Kenneth M. Hanson

Los Alamos National Laboratory

### Abstract

An optimal solution to the problem of making binary decisions about a local region of a reconstruction is provided by the Bayesian method. The decision is made on the basis of the ratio of the posterior probabilities for the two hypotheses. The full Bayesian procedure requires an integration of the posterior probability over all possible values of the image outside the local region being analyzed. In the present work, this full treatment is replaced by the minimum value of the posterior probability obtained when the exterior region is varied, but the interior is fixed at both hypothesized functional forms. A Monte Carlo procedure is employed to evaluate the usefulness of the technique in a signal-known-exactly detection task in a noisy four-view tomographic reconstruction situation.

**Keywords:** binary decision, Receiver Operating Charactersitic (ROC), machine observer, detectability, Bayesian reconstruction, posterior probability, generalized posterior-probability ratio, limited-angle tomographic reconstruction

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