Measurement bounds for sparse signal ensembles via graphical models

Marco F. Duarte, Michael B. Wakin, Dror Baron, Shriram Sarvotham, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing extends this framework by defining ensemble sparsity models, allowing a correlated ensemble of sparse signals to be jointly recovered from a collection of separately acquired compressive measurements. In this paper, we introduce a framework for modeling sparse signal ensembles that quantifies the intra- and intersignal dependences within and among the signals. This framework is based on a novel bipartite graph representation that links the sparse signal coefficients with the measurements obtained for each signal. Using our framework, we provide fundamental bounds on the number of noiseless measurements that each sensor must collect to ensure that the signals are jointly recoverable.

Original languageEnglish (US)
Article number6502243
Pages (from-to)4280-4289
Number of pages10
JournalIEEE Transactions on Information Theory
Volume59
Issue number7
DOIs
StatePublished - Jul 2013

Keywords

  • Compressive sensing (CS)
  • Random projections
  • Signal ensembles
  • Sparsity

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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