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

University Of California-San Diego, La Jolla CA

Investigators

Abstract

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.