The authors previously described how image reconstruction algorithms can be evaluated on the basis of how well binary-discrimination tasks can be performed using the reconstructions. The test statistic in the detection task was the estimated activity within the object, also known as the non-prewhitening matched-filter output. This approximation to the likelihood function was used because a full characterization of the posterior probability function had not yet been performed. A more complete approach is possible when the reconstruction procedure is founded on the Bayesian method. In this case the reconstruction is chosen to maximize the posterior probability and task performance involves using the posterior probability of the various alternatives as the decision variable. This full Bayesian approach should lead to optimal results because the posterior probability incorporates the full dependence on the measurements and constraints, yet is based on the relatively simple likelihood and prior probability distributions. The commercially available code MEMSYS 3 provides Bayesian image reconstructions based on an entropy prior. This paper details a method of image reconstruction evaluation based on the full posterior probability ratio, and describes results obtained using images derived from the MEMSYS 3 algorithm for a simple binary detection task. The results demonstrate the improvement in detection performance that can be achieved when the full posterior probability function is incorporated into the decision variable.
Keywords: reconstruction comparison, reconstruction evaluation, reconstruction optimization, task performance, detectability index, figure of merit, machine observer, maximum-entropy reconstruction, MEMSYS 3, algebraic reconstruction technique (ART)
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