Methods of Harmonic Analysis for Threat Detection

在这项研究中，研究人员创建了用于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风险。化学或生物事件的早期和准确检测、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允许快速部署传感器，并提高收集监视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已无法满足众多需求和不断变化的环境，也无法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，可以解决我们在威胁检测中面临的新挑战。特别是研究人员将专注于高光谱传感模式和层析化学蒸汽检测的高效，稳健和可扩展的算法的开发。这项研究利用了谐波分析，优化和信号处理的最新进展。数学工具将包括稀疏表示和压缩感知，随机矩阵理论，几何功能分析和数值分析。该项目的成功可以基于研究人员在开发先进的数学概念并将其转化为现实世界应用方面的现有坚实成就。这项研究活动将以快速有效的数值算法的形式在国防和安全部门实现进一步的进步和突破，用于通过远距离传感器模式检测化学和生物制剂。拟议的研究是尖端数学的几个领域与最先进的威胁检测技术的结合。这一努力的一个重要部分是调查员与威胁探测实际方面的专家密切合作。威胁检测实验的真实的世界数据将被用于本研究，既验证所开发的方法，并改善数学建模。除了该项目的广泛的技术影响，它作为一种跨学科的活动，在数学/工程前沿的研究和教育至关重要的模式。因此，这项研究工作有助于培养研究生数学发展和提高技能，是至关重要的，迫切需要在一个高科技为导向的社会。

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.