ATD: Frame-Theoretic Algorithms for Smart Sensing

ATD：智能传感框架理论算法

• 批准号: 1321779
• 负责人: Peter Casazza
• 金额: $ 108.59万
• 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: 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=1321779&HistoricalAwards=false
• 关键词: ATD; Frame; Theoretic; Algorithms; Smart

The investigators design explicit sensing matrices in concert with signal processing algorithms that outperform the state of the art. They progress towards solutions of several of the most significant open problems in compressed sensing and frame theory: (a) to find deterministic constructions of matrices with the restricted isometry property (RIP); (b) to construct real and complex equiangular tight frames (ETFs), including the maximal ETFs conjectured to exist by Zauner; (c) to design fast and reliable algorithms for phase retrieval;(d) to prove recent refinements of Wright's conjecture regarding the minimal number of injective intensity measurements; (e) the Paulsen problem: How to project onto the manifold of unit norm tight frames (UNTFs).Threat detection requires high-quality sensing and effective signal processing algorithms. Most modern threats have faint signatures, leaving intelligence agencies with two main problems. First, you can't find what you don't seek. That is, in order to detect a threat, you must first adequately sense the region of interest. Because of this, part of the work focuses on new mathematics that will improve sensing capabilities. This has the unfortunate side-effect of adding to the existing fire hose of data, exacerbating the second main problem: "finding a needle in a haystack." At the moment, analysts must wade through unimaginably large data sets in order to extract actionable intelligence. As such, the remainder of the work focuses on new mathematical ways of processing big data sets.

研究人员设计显式传感矩阵与信号处理算法，超越了最先进的状态。他们的进展对压缩感知和框架理论中的几个最重要的开放问题的解决方案：（a）找到具有限制等距属性（RIP）的矩阵的确定性结构;（B）构造真实的和复等角紧框架（ETFs），包括Zauner证明存在的最大ETFs：（c）设计快速可靠的相位恢复算法;（d）证明Wright关于最小数量的单射强度测量的猜想的最新改进;（e）Paulsen问题：如何投影到单位范数紧框架（UNTF）的流形上。威胁检测需要高质量的传感和有效的信号处理算法。 大多数现代威胁的特征都很模糊，这给情报机构带来了两个主要问题。 首先，你找不到你不寻找的东西。 也就是说，为了检测威胁，您必须首先充分感知感兴趣的区域。 正因为如此，部分工作集中在新的数学，将提高传感能力。 这有一个不幸的副作用，增加了现有的数据消防水带，加剧了第二个主要问题：“大海捞针。“目前，分析师必须费力地通过庞大的数据集，以提取可操作的情报。 因此，剩下的工作集中在处理大数据集的新数学方法上。