Compressed Sensing with Combinatorial Designs: Theory and Simulations

Darryn Bryant, Charles Colbourn, Daniel Horsley, Padraig O Cathain

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We use deterministic and probabilistic methods to analyze the performance of compressed sensing matrices constructed from Hadamard matrices and pairwise balanced designs, previously introduced by a subset of the authors. In this paper, we obtain upper and lower bounds on the sparsity of signals for which our matrices guarantee recovery. These bounds are tight to within a multiplicative factor of at most. We provide new theoretical results and detailed simulations, which indicate that the construction is competitive with Gaussian random matrices, and that recovery is tolerant to noise. A new recovery algorithm tailored to the construction is also given.

Original languageEnglish (US)
Article number7954982
Pages (from-to)4850-4859
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2017


  • Combinatorial designs
  • Compressed sensing
  • Signal recovery

ASJC Scopus subject areas

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


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