Compressive detection and estimation

The results of compressive sensing have inspired the design of physical systems that directly implement random measurement schemes. However, despite the intense focus on the reconstruction of signals, many (if not most) signal processing problems do not require a full reconstruction of the signal -- we are often interested only in solving some sort of detection problem or in the estimation of some function of the data. We show that the compressed sensing framework is useful for a wide range of statistical inference tasks. In particular, we demonstrate how to solve a variety of signal detection and estimation problems given the measurements without ever reconstructing the signals themselves. We provide theoretical bounds along with experimental results.

Authors: Mark Davenport, Micahel Wakin, Richard Baraniuk

Publications: Technical Report

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