CIF: Small: Reconstructing Multiple Sources by Spatial Sampling and Compression

CIF：小：通过空间采样和压缩重建多个源

• 批准号: 1910497
• 负责人: Prakash Narayan
• 金额: $ 47.5万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-10-01 至 2023-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1910497&HistoricalAwards=false
• 关键词: CIF; Small; Reconstructing; Multiple; Sources

The mathematics of signal processing underlies much of the modern digital world today. Digital signal processing relies on a technique called sampling, that allows information to be gathered about the underlying signal using a subset of samples from the signal, and information theory is used to describe fundamental principles of sampling. This project takes an information theoretic approach to develop fundamental principles that govern sampling of a small subset of a much larger set of correlated signals and processing them efficiently in order to reconstruct accurately a desired larger group of signals. These principles will be useful in myriad applications, for instance, in: potential smart homes with multiple networked smart sensor devices operating under transmitter power and channel bandwidth limitations; aerial surveillance systems for monitoring city traffic patterns or forest covers in which sources of information far outnumber the unmanned aerial vehicles or satellites that can be deployed; computer vision systems where data obtained from a limited camera scan and sensing must be interpolated to form a larger picture; and spotting trends in large social networks by polling small groups and gathering contextual data.The tasks the signal processing system is to perform include: limited random sampling of spatially correlated time-signals; compress the samples for efficient channel transmission or storage; and recover, by decompression, a desired larger subset of the original signals with high accuracy. Optimality of such signal processing relies crucially on methods for estimating the unknown statistical behavior of the joint signals. A common framework will be developed for analyzing interwoven concepts of spatial signal sampling, estimation of joint signal statistics, lossy compression and signal reconstruction. New information theoretic formulations and approaches will be developed in this project with the objective of understanding basic underlying principles that will lead to implementable signal processing algorithms. The technical approach involves the development of a theory for signal processing with three main distinguishing features: (i) coordinated random spatial sampling of subsets of multiple correlated signals; (ii) statistical learning of unknown signal probability distributions; and (iii) universal rate-efficient lossy compression of sampled signals followed by reconstruction. The objective is to reconstruct a predesignated subset of signals with a specified level of accuracy. Processing of the signals must be universal in that the combined sampling, learning and compression must be robust in the face of inexact prior knowledge of the underlying probability distribution of the signals. Rooted in information theory, this research project also explores innate connections to joint probability distribution learning (in statistical learning theory) and correlated multi-armed bandits (in machine learning). The larger goal of the project is to understand connections among universal spatial sampling, distribution learning and compression rate-distortion performance. Furthermore, it aims to create advances in information theory through the introduction of new models and concepts, and in probability distribution learning and machine learning through new formulations and solutions. Expected outcomes are new techniques for joint distribution learning; and a characterization of fundamental performance limits and the structure of optimal universal sampling and compression that will guide algorithm design.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.

信号处理的数学是当今现代数字世界的基础。数字信号处理依赖于一种称为采样的技术，该技术允许使用信号样本的子集来收集有关基础信号的信息，并且信息论用于描述采样的基本原理。该项目采用信息论方法来开发基本原理，这些原理控制对更大的一组相关信号的小子集的采样并有效地处理它们，以便准确地重建所需的更大的信号组。这些原理将在多种应用中发挥作用，例如：具有在发射器功率和通道带宽限制下运行的多个联网智能传感器设备的潜在智能家居；用于监测城市交通模式或森林覆盖的空中监视系统，其信息来源远远超过可部署的无人驾驶飞行器或卫星；计算机视觉系统，从有限的相机扫描和感测获得的数据必须进行插值以形成更大的图像；信号处理系统要执行的任务包括： 对空间相关的时间信号进行有限随机采样；压缩样本以实现高效的通道传输或存储；并通过解压缩以高精度恢复原始信号的所需较大子集。这种信号处理的最优性主要依赖于估计联合信号的未知统计行为的方法。将开发一个通用框架来分析空间信号采样、联合信号统计估计、有损压缩和信号重建等相互交织的概念。该项目将开发新的信息论公式和方法，目的是理解基本原理，从而实现可实现的信号处理算法。该技术方法涉及信号处理理论的发展，该理论具有三个主要显着特征：（i）多个相关信号子集的协调随机空间采样； (ii) 未知信号概率分布的统计学习； (iii) 采样信号的通用速率高效有损压缩，随后进行重建。目标是以指定的精度水平重建预先指定的信号子集。信号的处理必须是通用的，因为组合的采样、学习和压缩在面对信号的潜在概率分布的不精确的先验知识时必须是鲁棒的。该研究项目植根于信息论，还探讨了联合概率分布学习（统计学习理论中）和相关多臂老虎机（机器学习中）的固有联系。该项目的更大目标是了解通用空间采样、分布学习和压缩率失真性能之间的联系。此外，它的目标是通过引入新的模型和概念来推动信息论的进步，并通过新的公式和解决方案来推动概率分布学习和机器学习的进步。预期成果是联合分布学习的新技术；该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Shared Information for the Cliqueylon Graph

Cliqueylon 图的共享信息

• DOI: 10.1109/isit54713.2023.10206503
• 发表时间: 2023
• 期刊: Proceedings of the 2023 IEEE Symposium on Information Theory
• 作者: Bhattacharya, Sagnik;Narayan, Prakash
• 通讯作者: Narayan, Prakash

Universal Single-Shot Sampling Rate Distortion

通用单次采样率失真

• DOI: 10.1109/isit45174.2021.9518150
• 发表时间: 2021
• 期刊: 2021 IEEE International Symposium on Information Theory
• 作者: Bhattacharya, Sagnik;Narayan, Prakash
• 通讯作者: Narayan, Prakash

Proceedings of the 2022 IEEE International Symposium on Information Theory

2022 年 IEEE 国际信息论研讨会论文集

• 发表时间: 2022
• 期刊: 2022 IEEE International Symposium on Information Theory/
• 作者: Sagnik Bhattacharya;Prakash Narayan
• 通讯作者: Prakash Narayan