CAREER: Smart Sampling and Correlation-Driven Inference for High Dimensional Signals

技术进步推动了现代传感系统产生海量数据，使得以具有成本效益和可靠的方式存储、传输和处理此类数据变得越来越具有挑战性。然而，许多信息处理任务的最终目标是推断一些感兴趣的参数，这些参数支配着数据的统计和物理模型。这包括从雷达和成像系统中的信号源定位到机器学习中推断潜在变量的各种应用。这类问题中的参数数量比采集的数据量小得多，这导致了更智能的方法来感测高维信号，其可以利用信号的统计模型(具有或不具有稀疏性)以及问题的物理。该项目的目标是为现代传感系统开发一种智能采样和信息检索算法的系统理论，该算法利用高维信号的相关结构来显著减少推断所需的测量数量。拟议的研究可以导致部署更少的传感器(比传统要求的传感器更少)，以及更节能的方式来收集和处理时空数据，这将对高分辨率成像、遥感、神经信号处理和无线通信等多个学科的应用产生积极影响。该项目的技术部分有三个相互关联的目标：(I)为利用统计和物理信号模型的相关感知采样器设计全新的几何形状；(Ii)开发和分析新的相关驱动算法的性能，以了解相关感知采样器的基本能力；以及(Iii)利用相关感知采样器背后的思想来开发更高效的算法来解决双线性和多线性问题。这些采样器的设计将为二次采样器的性质提供新的理论见解，并将有助于解决可能独立感兴趣的基本数学问题。采样器还促进了新推理策略的开发，对这些算法提出的严格的理论分析有望从根本上促进我们目前对压缩数据参数估计的局限性的理解。最后，相关感知采样器背后的想法与机器学习中的问题有很强的联系，如词典学习和潜在变量分析，它们将促进这些领域未来的研究进展。

Technological advances have driven modern sensing systems towards generating massive amounts of data, making it increasingly challenging to store, transmit and process such data in a cost effective and reliable manner. However, the ultimate goal in many information-processing tasks is to infer some parameters of interest, that govern the statistical and physical model of the data. This includes applications ranging from source localization in radar and imaging systems to inferring latent variables in machine learning. The number of parameters in such problems is much smaller than the acquired volume of data, which leads to the possibility of more intelligent ways of sensing high dimensional signals, that can exploit the statistical model of the signal (with or without invoking sparsity), and the physics of the problem. The objective of this project is to develop a systematic theory of smart sampling and information retrieval algorithms for modern sensing systems that exploit the correlation structure of high dimensional signals to significantly reduce the number of measurements needed for inference. The proposed research can lead to deployment of fewer sensors (than what is traditionally required), as well as more energy efficient ways to collect and process spatio-temporal data that will positively impact a number of applications across disciplines, such as, high resolution imaging, remote sensing, neural signal processing and wireless communication. The educational component of this project aims at integrating the research outcomes into innovative teaching platforms such as ''Sense Smarter'', and ''Signals Everywhere'' that will help train the next generation of electrical engineers, and encourage them to pursue careers in STEM fields.The technical component of the project has three interconnected goals: (i) designing fundamentally new geometries for correlation-aware samplers that exploit the statistical as well as physical signal models, (ii) developing, and analyzing the performance of new correlation driven algorithms to understand fundamental capabilities of correlation-aware samplers, and (iii) exploiting the ideas behind correlation-aware samplers to develop more efficient algorithms for solving bi- and multi-linear problems. Design of these samplers will provide new theoretical insights into properties of quadratic samplers, and will help address fundamental mathematical questions that can be of independent interest. The samplers also facilitate the development of new inference strategies, and the proposed rigorous theoretical analysis of these algorithms is expected to fundamentally advance our current understanding of the limits of parameter estimation from compressed data. Finally, the ideas behind correlation-aware samplers have strong connections with problems in machine learning such as dictionary learning, and latent variable analysis, and they will foster future research advances in these areas.