Mathematical Foundation for Signal Processing on Spatially Distributed Networks

空间分布的数据网络由大量具有数据收集、处理和共享能力的协作代理组成。 它已被广泛应用于（无线）传感器网络，智能电网和其他工程和科学领域，因为它提供了一些实际的优势，比传统形式的数据网络，船舶收集的数据到中央处理设施。 然而，分布数据处理任务，如滤波，去噪和压缩，提出了一些新的挑战。 虽然这些近年来受到了广泛的关注，但数学理论与工程实践之间仍然存在差距。 该研究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，这些数据网络对工程应用具有实际影响。 研究生参与研究。 研究生参与了研究工作，用稀疏图描述了空间分布数据网络的拓扑结构。 空间分布数据网络上的数据处理由网络中的代理执行;其中许多可以通过良好的局部化矩阵和积分算子来描述，原则上可以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。 主要研究人员研究如何将一个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，他的目标是为具有工程应用的此类网络上的信号处理开发数学基础。 在这里，他强调应用谐波分析和数值分析的局部化矩阵的图形，设计稳定的空间分布式数据网络，快速算法实现的代理在空间分布式数据网络，无相信号重建，以及深度学习耦合到信号处理的图形。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.