ATD: Frame-Theoretic Information Fusion for Threat Detection

ATD：用于威胁检测的框架理论信息融合

• 批准号: 1042701
• 负责人: Peter Casazza
• 金额: $ 91.95万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2014-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1042701&HistoricalAwards=false
• 关键词: ATD; Frame; Theoretic; Information; Fusion

This project addresses several emerging problems in the mathematical field of Hilbert space frames. This research has two thrusts. The first thrust involves using frame theory to provide sparse representations of data. Here, the project is concerned with the paramount problems of the field: to provide verifiable constructions of restricted isometry property (RIP) matrices of implementable size; to find algorithmic constructions of real and complex Grassmannian frames; to find frames which, in the sparsest possible manner, represent a given set of data. The second thrust involves using frame theory to fuse information gathered from disparate sensor modalities. Here, the work focuses on several fundamental open problems of multimodal data processing, such as how to mathematically determine what given collections of modalities yields optimal detection accuracies, and how data from different modes should be registered.Recent advances in sensor hardware provide an unprecedented capability to detect the production, deployment and use of chemical and biological weapons. At the same time, the cost of misdetecting such threats is extremely high. Moreover, human intelligence analysts are increasingly overwhelmed by ever-larger data sets. The purpose of this project is to develop new mathematics which will help automate as much of this threat detection process as is possible, freeing human analysts to focus on the most high-level tasks. In particular, a good understanding of sparse representations allows one to break very complicated phenomena into a relatively small number of much-easier-to-understand pieces. Meanwhile, a good understanding of multimodal data allows one to combine data from many different sensors, in order to make a decision which is wiser than could be made from the data of any single sensor alone.

该项目解决了希尔伯特空间框架数学领域中的几个新兴问题。 这项研究有两个重点。 第一个推力涉及使用框架理论提供数据的稀疏表示。 在这里，该项目关注的是该领域的首要问题：提供可实现的大小的限制等距属性（RIP）矩阵的可验证结构;找到真实的和复杂的格拉斯曼框架的算法结构;找到以稀疏可能的方式表示给定数据集的框架。 第二个推力涉及使用框架理论融合从不同的传感器模态收集的信息。 在这里，工作集中在几个基本的开放问题的多模态数据处理，如如何在数学上确定什么给定的集合的方式产生最佳的检测精度，以及如何从不同的模式的数据应registered. Recent advances in sensor hardware provides a unprecedented capability to detect the production，deployment and use of chemical and biological weapons. 与此同时，误判这种威胁的代价也非常高。 此外，人类情报分析师越来越被越来越大的数据集所淹没。 该项目的目的是开发新的数学，这将有助于尽可能多地自动化威胁检测过程，使人类分析师能够专注于最高级别的任务。 特别是，对稀疏表示的良好理解允许人们将非常复杂的现象分解为相对较少的更容易理解的片段。 同时，对多模态数据的良好理解允许人们将来自许多不同传感器的数据联合收割机组合，以便做出比单独从任何单个传感器的数据做出的决策更明智的决策。