An asymptotic existence result on compressed sensing matrices

Bryant, Darryn and Catháin, Padraig Ó. (2015) An asymptotic existence result on compressed sensing matrices. Linear Algebra and Its Applications, 475 134-150. doi:10.1016/j.laa.2015.02.010

Author Bryant, Darryn
Catháin, Padraig Ó.
Title An asymptotic existence result on compressed sensing matrices
Journal name Linear Algebra and Its Applications   Check publisher's open access policy
ISSN 0024-3795
Publication date 2015-06-15
Sub-type Article (original research)
DOI 10.1016/j.laa.2015.02.010
Volume 475
Start page 134
End page 150
Total pages 17
Place of publication Philadelphia, PA, United States
Publisher Elsevier
Collection year 2016
Language eng
Formatted abstract
For any rational number h and all sufficiently large n we give a deterministic construction for an n×⌊hn⌋ compressed sensing matrix with (ℓ1,t)-recoverability where t = O(n). Our method uses pairwise balanced designs and complex Hadamard matrices in the construction of ϵ -equiangular frames, which we introduce as a generalisation of equiangular tight frames. The method is general and produces good compressed sensing matrices from any appropriately chosen pairwise balanced design. The (ℓ1,t)-recoverability performance is specified as a simple function of the parameters of the design. To obtain our asymptotic existence result we prove new results on the existence of pairwise balanced designs in which the numbers of blocks of each size are specified.
Keyword Compressed sensing
Pairwise balanced designs
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 3 times in Scopus Article | Citations
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