Sample Abundance for Signal Processing: A Brief Introduction

Abstract: This paper reports, by way of introduction, on the advances made by our group and the broader signal processing community on the concept of sample abundance; a phenomenon that naturally arises in one-bit and few-bit signal processing frameworks. By leveraging large volumes of low-precision measurements, we show how traditionally costly constraints, such as matrix semi-definiteness and rank conditions, become redundant, yielding simple overdetermined linear feasibility problems. We illustrate key algorithms, theoretical guarantees via the Finite Volume Property, and the sample abundance singularity phenomenon, where computational complexity sharply drops.