On the rate-distortion performance of compressed sensing

Alyson K. Fletcher, Sundeep Rangan, Vivek K. Goyal

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

Abstract

Encouraging recent results in compressed sensing or compressive sampling suggest that a set of inner products with random measurement vectors forms a good representation of a source vector that is known to be sparse in some fixed basis. With quantization of these inner products, the encoding can be considered universal for sparse signals with known sparsity level. We analyze the operational rate-distortion performance of such source coding both with genie-aided knowledge of the sparsity pattern and maximum likelihood estimation of the sparsity pattern. We show that random measurements induce an additive logarithmic rate penalty, i.e., at high rates the performance with rate R + O(log R) and random measurements is equal to the performance with rate R and deterministic measure-ments matched to the source.

Original languageEnglish (US)
Title of host publication2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07
PagesIII885-III888
DOIs
StatePublished - 2007
Event2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07 - Honolulu, HI, United States
Duration: Apr 15 2007Apr 20 2007

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume3
ISSN (Print)1520-6149

Other

Other2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07
CountryUnited States
CityHonolulu, HI
Period4/15/074/20/07

Keywords

  • Compressed sensing
  • Eigenvalue distribution
  • Quantization
  • Random matrices
  • Subspace detection

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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