Multiscale hypothesis testing with application to anomaly characterization from tomographic projections

A common objective in many applied problems is to infer properties of the interior of an object based on tomographic (line-integral) projections. In a number of applications the ultimate goal is to characterize (e.g., detect, locate) regions of the interior which are, in some sense, anomalous. A major challenge is to develop methods which can characterize anomalies directly in the data domain (i.e., without image reconstruction). In this thesis we develop data domain techniques for the detection and localization of a single anomaly from tomographic projections. These techniques are based upon a multiscale hypothesis test (MSHT) framework. A MSHT represents an efficient alternative to a very large conventional hypothesis test which may be computationally infeasible due to the overwhelming number of hypotheses which must be considered. Previous application of MSHTs to anomaly localization problems has focussed on the intuitive idea of spatial zooming with natural statistics [19-21]. A major contribution of this thesis is the broader interpretation of multiscale hypothesis testing as statistical zooming on the set of hypotheses rather than spatial zooming in the image domain. This broader interpretation leads naturally to the formulation of an optimization problem, the solution of which provides a MSHT statistic which yields improved performance. Thesis Supervisor: Alan S. Willsky Title: Professor of Electrical Engineering Thesis Supervisor: W. Clem Karl Title: Research Affiliate