Methods and Algorithms from Harmonic Analysis for Threat Detection

用于威胁检测的谐波分析方法和算法

• 批准号: 1322393
• 负责人: Thomas Strohmer
• 金额: $ 102.02万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1322393&HistoricalAwards=false
• 关键词: Methods; Algorithms; Harmonic; Analysis; Threat; Methods; Algorithms; Harmonic; Analysis; Threat

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.

研究人员开发了新的数学概念和威胁检测的数值方法。对化学或生物学威胁的早期和准确检测对于有效反应至关重要。在许多情况下，当前用于威胁检测的算法和传感器不再能够跟上众多需求和不断变化的环境以及需要处理和分析的大量数据以完成这些任务。这项研究工作的目的是开发新颖的数学概念和计算方法，以应对我们在威胁检测中面临的新挑战。特别是，研究者将着重于多光谱传感方式的高效，健壮和可扩展算法的开发以及通过Terahertz成像进行威胁检测。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，压缩传感和矩阵完成，随机矩阵理论，几何功能分析和数值分析。这项研究工作的两个具体主题是：（i）开发高度元素成像中有效获取，重建和变化检测的方法； （ii）构建Terahertz成像系统和随附的数值图像重建方法。此处提出的研究是尖端数学领域与最先进的威胁检测技术的婚姻，他们试图以快速有效的计算方法的形式将应用的和谐分析的先进技术从应用和安全部门带到防御和安全部门。这项研究工作的一个重要部分是研究人员与专家在威胁检测的实际方面的密切合作。这项研究将使用来自威胁检测实验的现实世界数据，既可以验证开发的方法又可以改善数学建模。对该项目成功的强烈期望可以基于研究人员在开发高级数学概念并将其转变为现实世界应用方面的现有扎实成就。除了该项目的广泛技术影响外，它还可以作为数学/工程前沿研究和教育至关重要的跨学科活动的模型。因此，这项研究工作有助于培训数学研究生，以发展和增强我们面向高科技的社会至关重要且急需的技能。