Optimal and Structured Frames with Applications

最佳结构化框架及应用

• 批准号: 1106934
• 负责人: Deguang Han
• 金额: $ 17.62万
• 依托单位: The University of Central Florida Board of Trustees
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106934&HistoricalAwards=false
• 关键词: Optimal; Structured; Frames; Applications

HanDMS-1106934 This project has three main goals: (i) Develop the theory and algorithms for optimal dual (and fusion) frames for erasures and for sparse signal reconstruction. (ii) Develop the theory of the frame spectrum for fractal measures that can provide much faster reconstruction (for example, compared to the classical Shannon sampling method) for functions that are concentrated on fractal-like regions. (iii) Investigate the connections between the Feichtinger frame conjecture for group representation frames and related problems such as the Kadison-Singer problem. In today's digital world efficient data processing has become more demanding in all kinds of applications. The principal investigator studies fundamental questions in harmonic and functional analysis that are applicable in areas such as wireless communications, radar, seismic sensing, image processing, reliable classification of features in biomedical images, and algorithms for the compensation of data loss in digital transmission of signals. The optimal dual frame design problems for erasures and sparsity are directly related to basic issues in redundant representation and transformation of signals. The investigation leads to applicable tools for problems in engineering and information applications, and provides theoretical analysis and algorithmic construction for computationally efficient frames.

本项目有三个主要目标：(i)开发用于擦除和稀疏信号重建的最佳对偶（和融合）帧的理论和算法。（ii）发展分形测量的框架谱理论，可以为集中在分形区域的函数提供更快的重建（例如，与经典的香农采样方法相比）。（iii）研究群表示框架的Feichtinger框架猜想与相关问题（如Kadison-Singer问题）之间的联系。在当今的数字世界中，各种应用对高效数据处理的要求越来越高。首席研究员研究谐波和功能分析中的基本问题，这些问题适用于无线通信，雷达，地震传感，图像处理，生物医学图像特征的可靠分类以及信号数字传输中数据丢失补偿的算法。擦除性和稀疏性的最优双框架设计问题直接关系到信号冗余表示和变换的基本问题。该研究为工程和信息应用中的问题提供了适用的工具，并为计算效率高的框架提供了理论分析和算法构建。