RUI: Development of Frame Extensions and Applications, III

RUI：框架扩展和应用程序的开发，III

• 批准号: 0709384
• 负责人: Shidong Li
• 金额: $ 14.7万
• 依托单位: San Francisco State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0709384&HistoricalAwards=false
• 关键词: RUI; Development; Frame; Extensions; Applications

Li0709384 The investigator studies extensions of frames and theirapplications in signal processing. A common problem inapplications is data fusion, the combination of data representingdifferent aspects of the same item. For example, in attemptingto sharpen a picture, treating the foreground and backgroundseparately may produce a better overall image. The investigatorstudies frame-theoretical formulations for data fusion,emphasizing applications in multi-spectral image fusion andrelated mathematical and computational issues. He also studiesfused parallel sparse representation using fusion frames,examining issues of optimality and expected computationalefficiency. Fusion frames are an extension of frames to dealwith a set of overlapping subspaces; the aim is to fuse togetherinformation from overlapping subspaces into the composite totalspace. Fused sparse representation involves ways to obtainsparse representations of a signal in (overlapping) subspaces ina parallel fashion followed by a fusion operation. Theinvestigator also studies pseudoframe duals of B-spline Rieszsequences having either minimum support or both minimum supportand maximum approximation order. Limiting behavior of the smallsupport of pseudoframe duals is considered. Here pseudoframeduals arise from a notion of pseudoframes for subspaces (PFFS). PFFSs are frame-like systems for the linear analysis andsynthesis of a subspace. They differ from frames in that bothanalysis and synthesis sequences are not necessarily contained inthe subspace. Signal processing generally refers to making the signal easyto handle or of better quality. It is everywhere seen in ourmodern society. In this project, the principal noveltiesintroduced to signal processing are a new frame-theoreticalapproach to data fusion applications and ideas of performing datacompression using a notion of fusion frames. Data fusioncombines data sampled in different ways or represnting differentaspects of an item in order to obtain a better representation ofthe item. The investigator aims at developing methods ofcombining images obtained in different type of cameras (such asinfrared and conventional) into one single image with allinformation presented. In particular, he works to provide acombined image of much greater precision without ad-hocprocedures of conventional techniques. Advances here areimportant for such areas of information technology as commercialimaging, geographic surveys, geographic survey, mapping, andsensor array data processing. Similarly, the investigatordevelops tools to improve the efficiency of data compression byreducing a costly compression task into a set of parallel smallertasks followed by a precise combination mechanism governed by thetheory of fusion frames. More generally, the methods canincrease the speed of information transmission in a broad rangeof communication and signal processing environments.

Li0709384研究帧的扩展及其在信号处理中的应用。应用程序中的一个常见问题是数据融合，即表示同一项目的不同方面的数据的组合。例如，在尝试锐化一张图片时，分开处理前景和背景可能会产生更好的整体图像。研究人员研究数据融合的框架理论公式，重点研究在多光谱图像融合中的应用以及相关的数学和计算问题。他还研究了使用融合框架的融合并行稀疏表示，考察了最优性和预期计算效率的问题。融合框架是框架的扩展，用于处理一组重叠的子空间，其目的是将重叠的子空间中的信息融合到复合总空间中。融合稀疏表示涉及以并行方式获得信号在(重叠)子空间中的稀疏表示的方法，然后进行融合操作。研究了具有最小支撑度或同时具有最小支撑度和最大逼近阶的B-Spline Riesz序列的伪帧对。考虑了伪框架对偶小支承的极限行为。这里，伪帧对偶产生于子空间的伪帧(PFF)的概念。PFFS是对子空间进行线性分析和综合的框架系统。它们与帧的不同之处在于，分析和合成序列都不一定包含在子空间中。信号处理一般是指使信号易于处理或具有更好的质量。在我们的现代社会中，它随处可见。在这个项目中，信号处理的主要创新是一种新的框架理论方法，用于数据融合应用，以及使用融合框架的概念来执行数据压缩的想法。数据融合将以不同方式采样或表示项目不同方面的数据组合在一起，以获得项目的更好表示。研究人员的目标是开发一种方法，将不同类型的相机(如红外线和常规相机)获得的图像组合成一张显示所有信息的单一图像。特别是，他致力于提供更高精度的组合图像，而不需要传统技术的繁琐程序。这方面的进展对商业成像、地理调查、地理调查、测绘和传感器阵列数据处理等信息技术领域非常重要。同样，研究人员开发工具来提高数据压缩的效率，方法是将代价高昂的压缩任务减少为一组并行的较小任务，然后根据融合框架理论建立精确的组合机制。更广泛地说，这些方法可以在广泛的通信和信号处理环境中提高信息传输的速度。