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

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2017年 / 63卷 / 08期

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

页码：4850 / 4859

页数：10

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