Signal Processing With Compressive Measurements

TLDR

Compressive sensing theory enables recovery of sparse signals from few linear measurements, with random projections being near‑optimal and inspiring hardware that implements such measurements, yet many signal‑processing tasks do not require full signal reconstruction. The paper aims to solve inference problems—detection, classification, estimation, and filtering—using only compressive measurements without ever reconstructing the signals. The authors develop and analyze methods that perform these inference tasks directly from compressed data, avoiding reconstruction. They provide theoretical bounds and experimental results that demonstrate the feasibility of compressive inference approaches.

Abstract

The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.