ATD: Frame-Theoretic Information Fusion for Threat Detection

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This project addresses several emerging problems in the mathematical field of Hilbert space frames. This research has two thrusts. The first thrust involves using frame theory to provide sparse representations of data. Here, the project is concerned with the paramount problems of the field: to provide verifiable constructions of restricted isometry property (RIP) matrices of implementable size; to find algorithmic constructions of real and complex Grassmannian frames; to find frames which, in the sparsest possible manner, represent a given set of data. The second thrust involves using frame theory to fuse information gathered from disparate sensor modalities. Here, the work focuses on several fundamental open problems of multimodal data processing, such as how to mathematically determine what given collections of modalities yields optimal detection accuracies, and how data from different modes should be registered.Recent advances in sensor hardware provide an unprecedented capability to detect the production, deployment and use of chemical and biological weapons. At the same time, the cost of misdetecting such threats is extremely high. Moreover, human intelligence analysts are increasingly overwhelmed by ever-larger data sets. The purpose of this project is to develop new mathematics which will help automate as much of this threat detection process as is possible, freeing human analysts to focus on the most high-level tasks. In particular, a good understanding of sparse representations allows one to break very complicated phenomena into a relatively small number of much-easier-to-understand pieces. Meanwhile, a good understanding of multimodal data allows one to combine data from many different sensors, in order to make a decision which is wiser than could be made from the data of any single sensor alone.