CIF: Small: Blind information measures for waves: a deterministic approach

该项目的重点是研究传感和通信背景下的信号表示和重建。信号的非冗余表示是有效地执行感知和实现最佳通信速率的关键问题。在许多实际场景中，人们会希望利用少量测量来执行感测，通常利用信号结构的部分或不完整知识。具体地，对于占用频谱带的不相交子间隔的信号，通常假定知道子带的数量和位置。本项目研究以执行稍大数量的测量为代价来放松这些假设的方法。这项研究有几个潜在的好处。结果将导致对最佳传感和通信架构的见解，以及提供这些架构的基本限制。该项目还引入了新的数学方法，并在为信息波动理论奠定基础的过程中，将信息理论、函数逼近和压缩传感联系起来。在教育方面，它让学生参与研究，并为代表性不足的群体进行招聘。该研究计划考虑使用确定性方法对信号进行最小冗余信息描述，而不假设任何先验频谱知识。它提供了一个新的自由度的概念，适合带限和多频带信号。它还将这一概念扩展到更高的维度，以获得空时传播信号的信息理论界。该项目的根源在于函数逼近的经典理论和信号重要传播模式的确定。该理论与压缩感知的最新进展有关，并提供了离散和连续信号以及确定性和概率结果的统一观点。该项目的基本成果与通信和遥感系统都有关。信息理论方法为在真实的系统中可以实现的目标提供了一个基线。

This project focuses on the study of signal representation and reconstruction in the context of sensing and communication. Non-redundant representation of signals is a key issue to perform sensing efficiently and to achieve optimal communication rates. In many practical scenarios, one would want to perform sensing with a small number of measurements, often with partial or incomplete knowledge of the structure of the signal. Specifically, for signals occupying disjoint sub-intervals of the spectral band, knowledge of the number and locations of the sub-bands is typically assumed. This project investigates ways to relax these assumptions at the cost of performing a slightly larger number of measurements. There are several potential benefits arising from this research. Results will lead to insights on optimal sensing and communication architectures, as well as provide fundamental limits of these architectures. The project also introduces new mathematical methods and, in laying the foundations for the wave theory of information, it draws connections between information theory, functional approximation, and compressed sensing. On the education front, it involves students in the research, as well as recruitment efforts for under-represented groups. The research plan considers a least-redundant informational description of signals using a deterministic approach and without assuming any prior spectral knowledge. It provides a new notion of degrees of freedom that suits both band-limited and multi-band signals. It also extends this notion to higher dimensions to obtain information-theoretic bounds for space-time propagating signals. The roots of the project are in the classical theory of functional approximation and in the determination of the significant propagation modes of signals. The theory is connected to recent advancements in compressed sensing, and provides a unifying view of discrete and continuous signals as well as deterministic and probabilistic results. The foundational results of the project are relevant to both communication and remote sensing systems. The information-theoretic approach provides a baseline for what can be achieved in real systems.