A Multiscale Hypothesis Testing Approach toAnomaly Detection and Localization From NoisyTomographic

| In this paper we investigate the problems of anomaly detection and localization from noisy tomographic data. These are characteristic of a class of problems which cannot be optimally solved because they involve hypothesis testing over hypothesis spaces with extremely large cardi-nality. Our multiscale hypothesis testing approach addresses the key issues associated with this class of problems. A multiscale hypothesis test is a hierarchical sequence of composite hypothesis tests which discards large portions of the hypothesis space with minimal computational burden and zooms in on the likely true hypothesis. For the anomaly detection and localization problems, hypothesis zooming corresponds to spatial zooming|anomalies are successively localized to ner and ner spatial scales. The key challenges we address include how to hierarchically divide a large hypothesis space and how to process the data at each stage of the hierarchy to decide which parts of the hypothesis space deserve more attention. To answer the former we draw on 1,7{10]. For the latter, we pose and solve a non-linear optimization problem for a decision statistic which maximally disambiguates composite hypotheses. With no more computational complexity, our optimized statistic shows substantial improvement over conventional approaches. We provide examples which demonstrate this and which quantify how much performance is sacriiced by the use of a sub-optimal method as compared to that achievable if the optimal approach were computationally feasible.