RUI: Development of Frame Extensions and Applications, III

Li0709384 研究了框架的扩展及其在信号处理中的应用。 应用中的一个常见问题是数据融合，即表示同一项目不同方面的数据的组合。 例如，在尝试锐化图片时，分别处理前景和背景可能会产生更好的整体图像。 本课程研究数据融合的框架理论公式，强调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，研究了最优性和预期计算效率的问题。 融合框架是框架的一种扩展，用于处理一组重叠的子空间，目的是将重叠子空间的信息融合到合成的总空间中。 融合稀疏表示涉及的方法，以获得稀疏表示的信号（重叠）子空间以并行的方式，其次是融合操作。 本文还研究了具有最小支集或同时具有最小支集和最大逼近阶的B样条Riesz序列的伪框架结构。 考虑了伪框架结构小支座的极限行为。 这里的伪框架是由子空间的伪框架（PFFS）的概念产生的。PFFS是一种对子空间进行线性分析和综合的框架式系统。 它们与框架的不同之处在于分析序列和合成序列不一定都包含在子空间中。 信号处理通常指的是使信号易于处理或具有更好的质量。 它在我们现代社会中随处可见。 在这个项目中，引入信号处理的主要创新是一种新的数据融合应用的框架理论方法和使用融合框架的概念进行压缩的想法。 数据融合将以不同方式采样的数据或表示项目不同方面的数据组合在一起，以获得更好的项目表示。 研究者的目的是开发方法结合不同类型的相机（如红外和常规）获得的图像到一个单一的图像与显示。 特别是，他致力于提供更高精度的组合图像，而无需传统技术的广告程序。 这方面的进展对信息技术领域如商业成像、地理调查、地理勘测、制图和传感器阵列数据处理等都很重要。 类似地，开发工具，以提高数据压缩的效率，通过减少一个昂贵的压缩任务到一组并行的小任务，其次是一个精确的组合机制由thefusion帧的理论。 更一般地说，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。

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.