Methods of Harmonic Analysis for Threat Detection

在这项研究中，研究者创造了威胁检测的数学概念和数值方法。化学和生物威胁对我国构成重大威胁。对化学或生物事件的早期准确检测、定性和预警对于有效应对至关重要。传感器技术的最新进展使传感器能够快速部署，并增加了收集监测数据的灵活性和机动性。与此同时，需要保护的环境的多样性正在增加。当前的威胁检测算法不再能够跟上众多需求和不断变化的环境，也不能充分利用未来传感器技术的能力。这项研究工作的目标是开发新的数学概念和计算方法，以解决我们在威胁检测中面临的新挑战。特别是研究者将专注于开发高效、稳健和可扩展的算法，用于高光谱传感模式和层析化学蒸汽检测。本研究利用了谐波分析、优化和信号处理方面的最新进展。数学工具将包括稀疏表示和压缩感知、随机矩阵理论、几何泛函分析和数值分析。研究者在发展先进的数学概念并将其转化为现实世界的应用方面取得了坚实的成就，对这个项目成功的强烈期望可以基于此。这项研究活动将使国防和安全部门进一步取得进展和突破，其形式是通过隔离传感器模式快速有效地检测化学和生物制剂的数值算法。提出的研究是几个领域的前沿数学与最先进的威胁检测技术的结合。这项工作的一个重要部分是调查员与专家在威胁检测的实际方面的密切合作。本研究将使用来自威胁检测实验的真实世界数据，以验证所开发的方法并改进数学模型。除了该项目广泛的技术影响之外，它还为数学/工程前沿的研究和教育提供了一种跨学科活动的模型。因此，这项研究工作有助于培养数学研究生，以发展和提高在高科技导向的社会中至关重要和迫切需要的技能。

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.