RUI: Development of Nonorthogonal Fusion Frames and Reflective Sensing with Applications

研究者开发了一种新的（非正交）融合框架，一种反射传感的概念，及其应用。它们源于对稀疏融合框架算子的需求，以便在一般分布式系统中实现有效的数据融合应用。项目的主题1定义了一个新的非正交融合框架。初步研究表明，在现有融合框架算子完全稀疏的情况下，新融合框架算子的矩阵表示可以是对角的。由于融合操作最终涉及到融合框架算子的逆，并且由于子空间变换在实际数据融合应用中通常不可用，因此具有稀疏或对角融合算子的新型融合框架变得至关重要。主题2研究了基于子空间上多个非正交投影的多融合框架的概念。几乎令人惊讶的是，在一个固有子空间上定义的新的多融合框架算子可以很容易地成为正的和可逆的。有许多理论问题有待了解。基于主题1和主题2的研究，主题3概述了反射传感和多重反射传感的概念。研究了它们在侧测层析成像和多径无线信号接收中的理论和应用。值得指出的是，基于研究者对子空间伪帧的早期工作，非正交投影算子的实现自然是可以实现的。该项目涉及信号处理应用。信号处理一般是指使信号易于处理或具有更好的质量。它在我们的现代社会随处可见。在这个项目中，引入信号处理的主要新颖之处是非正交融合框架的新概念和执行数据融合的想法，例如，从多个路径接收的无线信号。融合框架是专门为各种数据融合应用开发的概念。数据融合是指将不同设备或不同手段测量到的数据结合起来，得到精细化的数据。非正交融合帧的优点在于，在实际的传感器网络中，特别是在数据量较大的情况下，它大大提高了数据融合过程的效率。该项目旨在开发有效的方法，将在信息覆盖（传感器之间）丰富且不可预测的传感器阵列中检测到的数据结合起来。在极其复杂的信息重叠情况下，通过非正交融合框架实现精确、高效的数据组合。特别是，该项目探索图像融合，以提供更高精度或分辨率的组合图像，而无需传统技术中存在的特别程序。数据融合问题出现在许多应用中，从商业成像到地理调查、制图、无线通信、多传感器/摄像机监控系统以及大量传感器网络应用。

LiDMS-1010058 The investigator develops a new (non-orthogonal) fusionframe, a notion of reflective sensing, and their applications. They are derived from the need for sparse fusion frame operatorsfor efficient data fusion applications in general distributedsystems. Theme 1 of the project defines a new non-orthogonalfusion frame. Preliminary studies show that the matrixrepresentation of the new fusion frame operator can be diagonalover the same example where the existing fusion frame operator iscompletely sparse-less. Because the fusion operation ultimatelyinvolves the inverse of the fusion frame operator, and becausesubspace transformations are generally unavailable in practicaldata fusion applications, such a new fusion frame with sparse ordiagonal fusion operator becomes crucial. Theme 2 studies anotion of multi-fusion frames based on multiple non-orthogonalprojections onto one subspace. Nearly surprisingly, the newmulti-fusion frame operator defined on one proper subspace can beeasily positive and invertible. A number of theoretical issuesare to be understood. Rooted in studies of themes 1 and 2, theme3 outlines a notion of reflective sensing and multiple reflectivesensing. Their theory and applications in side-measuredtomography and multi-path wireless signal receiving are examined. It is relevant to point out that the implementation ofnon-orthogonal projection operators is naturally achievable,based on earlier work by the investigator on pseudoframes forsubspaces. The project relates to signal processing applications. Signal processing generally refers to making the signal easy tohandle or of better quality. It is everywhere seen in our modernsociety. In this project, the principal novelties introduced tosignal processing are the new notion of non-orthogonal fusionframes and ideas of performing data fusion from, e.g., wirelesssignals received from multiple paths. Fusion frame is a notiondeveloped specifically for various data fusion applications. Data fusion means combining data measured by different devices orby different means in order to obtain refined data. Theadvantage of non-orthogonal fusion frames lies in the fact thatthey greatly improve efficiency of the data fusion procedure inpractical sensor networks, particularly when the amount of datais large. The project aims to develop effective methods ofcombining data detected in an array of sensors where informationoverlay (among sensors) is abundant and unpredictable. Withextremely complicated information overlaps, exact and efficientdata combination is made possible by non-orthogonal fusionframes. In particular, the project explores image fusion toprovide a combined image of much greater precision or resolutionwithout ad-hoc procedures present in conventional techniques. Data fusion problems arise in many applications, ranging fromcommercial imaging to geographic survey, mapping, wirelesscommunication, multi-sensor/camera surveillance systems, and agreat number of sensor network applications.