Compressed sensing with combinatorial designs: theory and simulations

Bryant, Darryn, Colbourn, Charles J., Horsley, Daniel and Cathain, Padraig O. (2017) Compressed sensing with combinatorial designs: theory and simulations. IEEE Transactions On Information Theory, 63 8: 4850-4859. doi:10.1109/TIT.2017.2717584

Author Bryant, Darryn
Colbourn, Charles J.
Horsley, Daniel
Cathain, Padraig O.
Title Compressed sensing with combinatorial designs: theory and simulations
Journal name IEEE Transactions On Information Theory   Check publisher's open access policy
ISSN 0018-9448
Publication date 2017-06-01
Sub-type Article (original research)
DOI 10.1109/TIT.2017.2717584
Open Access Status Not yet assessed
Volume 63
Issue 8
Start page 4850
End page 4859
Total pages 10
Place of publication Piscataway, NJ 08854 United States
Publisher Institute of Electrical and Electronics Engineers
Language eng
Subject 1710 Information Systems
1706 Computer Science Applications
3309 Library and Information Sciences
Abstract 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.
Keyword Compressed sensing
Combinatorial designs
Signal recovery
Q-Index Code C1
Q-Index Status Provisional Code
Grant ID DP120103067
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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