Compressive sensing matrices and hash families

Charles Colbourn, Daniel Horsley, Christopher McLean

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Deterministic construction of measurement matrices for compressive sensing can be effected by first constructing a relatively small matrix explicitly, and then inflating it using a column replacement technique to form a large measurement matrix that supports at least the same level of sparsity. In particular, using easily developed null space conditions for ℓ0- and ℓ1-recoverability, properties of the pattern matrix used to select columns lead to well-studied matrices, separating and distributing hash families. Two-stage compression and recovery techniques are developed that employ more computationally intensive ℓ0-recoverability for small matrices and simpler ℓ1-recoverability for one larger matrix; this can reduce the number of measurements required.

Original languageEnglish (US)
Article number5773644
Pages (from-to)1840-1845
Number of pages6
JournalIEEE Transactions on Communications
Issue number7
StatePublished - Jul 2011


  • Data compression
  • combinatorial mathematics
  • signal processing

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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