Methods and Algorithms from Harmonic Analysis for Threat Detection

点击翻译按钮获取中文摘要

The investigator develops new mathematical concepts and numerical methods for threat detection. Early and accurate detection of a chemical or biological threat are critical to an effective response. Current algorithms and sensors for threat detection are in many cases no longer able to keep up with the numerous demands and changing environments as well as the huge amounts of data that need to be processed and analyzed in order to accomplish these tasks. 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 multispectral sensing modalities and for threat detection via terahertz imaging. This research exploits recent advances in harmonic analysis, optimization, and signal processing. The mathematical tools will include sparse representations, compressive sensing and matrix completion, random matrix theory, geometrical functional analysis, and numerical analysis. Two concrete topics of this research effort are: (i) Development of methods for efficient acquisition, reconstruction and change detection in hyperspectral imaging; (ii) Construction of terahertz imaging system and accompanying numerical image reconstruction methods.The research proposed here is a marriage of several areas of cutting edge mathematics with state-of-the-art threat detection technology, seeking to bring advanced techniques from applied harmonic analysis to the Defense and Security sector in form of fast and efficient computational methods. An important part of this research 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. 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. 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 our high-tech oriented society.