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Mathematical Foundation for Signal Processing on Spatially Distributed Networks

空间分布式网络信号处理的数学基础

基本信息

批准号：
1816313
负责人：
Qiyu Sun
金额：
$ 19.52万
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：
2018
资助国家：
美国
起止时间：
2018-09-01 至 2022-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1816313&HistoricalAwards=false
关键词：
Mathematical Foundation Signal Processing Spatially

项目摘要

A spatially distributed data network consists of a large number of cooperative agents that have data collecting, processing, and sharing capabilities. It has been widely used in (wireless) sensor networks, smart power grids, and other engineering and science fields, because it offers some practical advantages over the more traditional form of data network that ships collected data to central processing facilities. However, distributing the data processing tasks, such as filtering, denoising, and compressing, raises some new challenges. While these have received much attention in recent years, there still is a gap between mathematical theory and engineering practice. The investigator works to develop a mathematical foundation for signal processing on spatially distributed data networks that has practical consequences for engineering applications. Graduate students participate in the research. Graduate students participate in the research.The topological structure of a spatially distributed data network is described by a sparse graph. Data processing on a spatially distributed data network is performed by agents in the network; many of them can be described by well-localized matrices and integral operators, in terms of which the network behavior can in principle be described and optimized globally. But this could be an impractically large optimization problem. The principal investigator studies how to split a large network into a set of overlapping smaller ones whose separate global optimizations can be used to approximate the global optimization of the large network. In this way, he aims to develop a mathematical foundation for signal processing on such networks that has engineering applications. Here he emphasizes applied harmonic analysis and numerical analysis of well-localized matrices on graphs, design of stable spatially distributed data networks, fast algorithms implemented by agents in spatially distributed data networks, phaseless signal reconstruction, and deep learning coupled to signal processing on graphs. Graduate students participate in the research.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

空间分布式数据网络由大量具有数据收集、处理和共享能力的协作主体组成。它已广泛应用于（无线）传感器网络、智能电网以及其他工程和科学领域，因为与将收集的数据发送到中央处理设施的更传统的数据网络形式相比，它具有一些实际优势。然而，分布式数据处理任务（例如过滤、去噪和压缩）提出了一些新的挑战。尽管这些近年来受到了广泛关注，但数学理论与工程实践之间仍然存在差距。研究人员致力于为空间分布式数据网络上的信号处理开发数学基础，这对工程应用具有实际意义。研究生参与研究。研究生参与研究。空间分布式数据网络的拓扑结构由稀疏图描述。空间分布式数据网络上的数据处理由网络中的代理进行；其中许多可以通过局部良好的矩阵和积分算子来描述，原则上可以在全局范围内描述和优化网络行为。但这可能是一个不切实际的大优化问题。主要研究者研究如何将大型网络拆分为一组重叠的较小网络，这些较小网络的单独全局优化可用于近似大型网络的全局优化。通过这种方式，他的目标是为此类网络上的信号处理建立具有工程应用的数学基础。在这里，他强调图上定位良好的矩阵的应用调和分析和数值分析、稳定的空间分布式数据网络的设计、空间分布式数据网络中的代理实现的快速算法、无相信号重建以及与图上的信号处理相结合的深度学习。研究生参与这项研究。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。