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Multiscale hypothesis testing with application to anomaly characterization from tomographic projections

Anomaly characterization from tomographic measurements is of interest in a wide range of fields. In this paper we address the problems of single anomaly detection and localization which we formulate as hypothesis testing problems. While the optimal hypothesis test is easy to formulate, it is computationally infeasible due to the overwhelming number of hypotheses which must be considered. We propose the multiscale hypothesis test (MSHT) as an efficient suboptimal alternative. We show how to find decision statistics to achieve maximal composite hypothesis distinguishability for the composite hypothesis tests which comprise the MSHT.