Measurements vs. Bits: Compressed Sensing meets Information Theory

Shriram Sarvotham, Dror Baron, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

74 Scopus citations

Abstract

Compressed sensing is a new framework for acquiring sparse signals based on the revelation that a small number of linear projections (measurements) of the signal contain enough information for its reconstruction. The foundation of Compressed sensing is built on the availability of noise-free measurements. However, measurement noise is unavoidable in analog systems and must be accounted for. We demonstrate that measurement noise is the crucial factor that dictates the number of measurements needed for reconstruction. To establish this result, we evaluate the information contained in the measurements by viewing the measurement system as an information theoretic channel. Combining the capacity of this channel with the rate-distortion function of the sparse signal, we lower bound the rate-distortion performance of a compressed sensing system. Our approach concisely captures the effect of measurement noise on the performance limits of signal reconstruction, thus enabling to benchmark the performance of specific reconstruction algorithms.

Original languageEnglish (US)
Title of host publication44th Annual Allerton Conference on Communication, Control, and Computing 2006
PublisherUniversity of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering
Pages1419-1423
Number of pages5
Volume3
ISBN (Print)9781604237924
StatePublished - 2006
Event44th Annual Allerton Conference on Communication, Control, and Computing 2006 - Monticello, United States
Duration: Sep 27 2006Sep 29 2006

Other

Other44th Annual Allerton Conference on Communication, Control, and Computing 2006
CountryUnited States
CityMonticello
Period9/27/069/29/06

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Networks and Communications

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