Compressed Sensing With Combinatorial Designs: Theory and Simulations

被引:11
|
作者
Bryant, Darryn [1 ]
Colbourn, Charles J. [2 ]
Horsley, Daniel [3 ]
Cathain, Padraig O. [4 ]
机构
[1] Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia
[2] Arizona State Univ, Sch Comp Informat & Decis Syst Engn, Tempe, AZ 85287 USA
[3] Monash Univ, Sch Math Sci, Melbourne, Vic 3800, Australia
[4] Worcester Polytech Inst, Sch Math Sci, Worcester, MA 01609 USA
基金
美国国家科学基金会; 澳大利亚研究理事会;
关键词
Compressed sensing; combinatorial designs; signal recovery; SIGNAL RECOVERY; MATRICES; CONSTRUCTIONS;
D O I
10.1109/TIT.2017.2717584
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
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 4 root 2. 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.
引用
收藏
页码:4850 / 4859
页数:10
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