Methods of Harmonic Analysis for Threat Detection

University Of California-Davis, Davis CA

Investigators

Abstract

In this research effort the investigator creates mathematical concepts and numerical methods for threat detection. Chemical and biological threats pose a significant risk to our country. Early and accurate detection, characterization and warning of a chemical or biological event are critical to an effective response. Recent advances in sensor technology allows for a rapid deployment of sensors and increased flexibility and mobility in gathering surveillance data. At the same time, the diversity of environments requiring protection is on the rise. Current algorithms for threat detection are no longer able to keep up with the numerous demands and changing environments, nor are they able to fully exploit the capabilities of future sensor technology. The goal of this research effort is to develop novel mathematical concepts and computational methods that can address the new challenges we are facing in threat detection. In particular the investigator will focus on the development of efficient, robust, and scalable algorithms for hyperspectral sensing modalities and for tomographic chemical vapor detection. This research exploits recent advances in harmonic analysis, optimization, and signal processing. The mathematical tools will include sparse representations and compressive sensing, random matrix theory, geometrical functional analysis, and numerical analysis. Strong expectation for success of this project can be based on existing solid achievements by the investigator in developing advanced mathematical concepts and turning them into real-world applications. This research activity will enable further advances and breakthroughs in the Defense and Security sector in the form of fast and efficient numerical algorithms for the detection of chemical and biological agents via stand-off sensor modalities. The proposed research is a marriage of several areas of cutting edge mathematics with state-of-the-art threat detection technology. An important part of this effort is the close collaboration of the investigator with experts in the practical aspects of threat detection. Real world data from threat detection experiments will be used in this research, both to validate the developed methods and to improve the mathematical modeling. Beyond the project's broad technological impact, it serves as a model for the kind of cross-disciplinary activity critical for research and education at the mathematics/engineering frontier. Hence this research effort helps to train graduate students in mathematics to develop and enhance skills that are crucial and urgently needed in a high-tech oriented society.