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

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中的样本子集来收集有关底层信号的信息，信息论用于描述采样的基本原理。该项目采用信息理论方法来开发基本原理，这些原理可以管理更大的相关信号集的一小部分采样，并有效地处理它们，以便准确地重建所需的更大的信号组。这些原则将在众多应用中发挥作用，例如：在发射机功率和信道带宽限制下，具有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；在计算机视觉系统中，从有限的相机扫描和传感中获得的数据必须内插以形成更大的图像；并通过调查小群体和收集相关数据来发现大型社交网络的趋势。信号处理系统要完成的任务包括：对空间相关时间信号进行有限随机采样；压缩样品以实现有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更大子集。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。新的信息理论公式和方法将在这个项目中发展，目的是理解基本的潜在原理，从而导致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，具有三个主要特征：(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，然后进行重构。目标是重建一个预先指定的信号子集，具有指定的精度水平。信号的处理必须是通用的，因为在面对信号潜在概率分布的不精确先验知识时，组合采样、学习和压缩必须是鲁棒的。基于信息论，该研究项目还探索了联合概率分布学习（统计学习理论）和相关多臂强盗（机器学习）之间的内在联系。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，它旨在通过引入新的模型和概念在信息论方面取得进展，并通过新的公式和解决方案在概率分布学习和机器学习方面取得进展。预期结果是联合分布学习的新技术；并描述了基本性能限制和最优通用采样和压缩的结构，这将指导算法设计。该奖项反映了美国国家科学基金会的法定使命，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。

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.