Signal processing with compressive measurements

Mark A. Davenport, Petros T. Boufounos, Michael B. Wakin, Richard G. Baraniuk

Research output: Contribution to journalArticle

466 Scopus citations

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 problemssuch as detection, classification, or estimationand filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.

Original languageEnglish (US)
Article number5419058
Pages (from-to)445-460
Number of pages16
JournalIEEE Journal on Selected Topics in Signal Processing
Volume4
Issue number2
DOIs
StatePublished - Apr 2010

Keywords

  • Compressive sensing (CS)
  • Compressive signal processing
  • Estimation
  • Filtering
  • Pattern classification
  • Random projections
  • Signal detection
  • Universal measurements

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

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