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

本项目致力于在感知和通信的背景下研究信号的表示和重构。信号的非冗余表示是有效执行侦听和获得最佳通信速率的关键问题。在许多实际场景中，人们可能希望使用少量的测量来执行感测，通常是在对信号结构的部分或不完全了解的情况下。具体地说，对于占据频谱带的不相交的子区间的信号，通常假定知道子带的数目和位置。这个项目研究了放松这些假设的方法，但代价是执行了稍微多一点的测量。这项研究带来了几个潜在的好处。结果将导致对最佳传感和通信体系结构的洞察，并提供这些体系结构的基本限制。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，将信息论、函数近似和压缩感知联系起来。在教育方面，它让学生参与研究，以及为代表性不足的群体进行招聘。该研究计划使用确定性方法来考虑信号的最小冗余信息描述，而不假设任何先验频谱知识。它提供了一种新的自由度概念，既适用于有限频带信号，也适用于多频带信号。它还将这一概念扩展到更高的维度，以获得时空传播信号的信息论界限。该项目的基础是经典的函数逼近理论和确定信号的重要传播模式。该理论与压缩传感领域的最新进展相联系，并提供了离散和连续信号以及确定性和概率结果的统一视图。该项目的基本成果与通信和遥感系统都有关。信息论方法为在实际系统中可以实现什么提供了基准。

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.