Estimation with random linear mixing, belief propagation and compressed sensing

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

Abstract

We apply Guo and Wang's relaxed belief propagation (BP) method to the estimation of a random vector from linear measurements followed by a componentwise probabilistic measurement channel. The relaxed BP method is a Gaussian approximation of standard BP that offers significant computational savings for dense measurement matrices. The main contribution of this paper is to extend Guo and Wang's relaxed BP method and analysis to general (non-AWGN) output channels. Specifically, we present detailed equations for implementing relaxed BP for general channels and show that the relaxed BP has an identical asymptotic large sparse limit behavior as standard BP as predicted by the Guo and Wang's state evolution (SE) equations. Applications are presented to compressed sensing and estimation with bounded noise.

Original languageEnglish (US)
Title of host publication2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
DOIs
StatePublished - 2010
Event44th Annual Conference on Information Sciences and Systems, CISS 2010 - Princeton, NJ, United States
Duration: Mar 17 2010Mar 19 2010

Publication series

Name2010 44th Annual Conference on Information Sciences and Systems, CISS 2010

Other

Other44th Annual Conference on Information Sciences and Systems, CISS 2010
CountryUnited States
CityPrinceton, NJ
Period3/17/103/19/10

Keywords

  • Belief propagation
  • Bounded noise
  • Compressed sensing
  • Density evolution
  • Non-Gaussian estimation
  • Sparsity

ASJC Scopus subject areas

  • Information Systems
  • Information Systems and Management

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  • Cite this

    Rangan, S. (2010). Estimation with random linear mixing, belief propagation and compressed sensing. In 2010 44th Annual Conference on Information Sciences and Systems, CISS 2010 [5464768] (2010 44th Annual Conference on Information Sciences and Systems, CISS 2010). https://doi.org/10.1109/CISS.2010.5464768