Methods and Algorithms from Harmonic Analysis for Threat Detection

研究人员开发了用于威胁检测的新的数学概念和数值方法。及早准确地检测到化学或生物威胁是有效应对的关键。当前用于威胁检测的算法和传感器在许多情况下不再能够跟上为完成这些任务而需要处理和分析的大量需求和不断变化的环境以及海量数据。这项研究的目标是开发新的数学概念和计算方法，以应对我们在威胁检测方面面临的新挑战。特别是，研究人员将专注于开发高效、健壮和可扩展的算法，用于多光谱传感模式和通过太赫兹成像进行威胁检测。这项研究利用了在谐波分析、优化和信号处理方面的最新进展。数学工具包括稀疏表示、压缩感知和矩阵补全、随机矩阵理论、几何泛函分析和数值分析。这项研究的两个具体主题是：(I)高光谱成像中高效采集、重建和变化检测的方法的发展；(Ii)太赫兹成像系统的构建和伴随的数字图像重建方法。这里提出的研究是几个前沿数学领域与最先进的威胁检测技术的结合，寻求以快速高效的计算方法将应用谐波分析的先进技术引入国防和安全部门。这项研究工作的一个重要部分是调查员与威胁检测实际方面的专家密切合作。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建模。对这个项目成功的强烈期望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现有的坚实成就。除了该项目广泛的技术影响外，它还是一种对数学/工程前沿的研究和教育至关重要的跨学科活动的典范。因此，这项研究工作有助于培养数学研究生，以发展和提高在我们这个以高科技为导向的社会中至关重要和迫切需要的技能。

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.