A MULTISCALE HYPOTHESIS-TESTING APPROACH TO ANOMALY DETECTION AND LOCALIZATION FROM NOISY TOMOGRAPHIC DATA

In this paper, we investigate the problems of anomaly detection and lo calization from noisy tomographic data. These are characteristic of a class of problems that cannot be optimally solved because they involve hypothesis testing over hypothesis spaces with extremely large cardin ality. Our multiscale hypothesis testing approach addresses the key is sues associated with this class of problems. A multiscale hypothesis t est is a hierarchical sequence of composite hypothesis tests that disc ards large portions of the hypothesis space with minimal computational burden and zooms in on the likely true hypothesis. For the anomaly de tection and localization problems, hypothesis zooming corresponds to s patial zooming-anomalies are successively localized to finer and finer spatial scales. The key challenges we address include how to hierarch ically divide a large hypothesis space and how to process the data at each stage of the hierarchy to decide which parts of the hypothesis sp ace deserve more attention. To answer the former we draw on [1] and [7 ]-[10], For the latter, we pose and solve a nonlinear optimization pro blem for a decision statistic that maximally disambiguates composite h ypotheses. With no more computational complexity, our optimized statis tic shows substantial improvement over conventional approaches. We pro vide examples that demonstrate this and quantify how much performance is sacrificed by the use of a suboptimal method as compared to that ac hievable if the optimal approach were computationally feasible.