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
收藏
页码：4850 / 4859
页数：10
相关论文
共 50 条
  • [31] Image information encryption by compressed sensing and optical theory
    Liu, Xiao-Yong, 1600, Chinese Optical Society (43):
  • [32] STUDY ON IMAGING SYSTEM BASED ON COMPRESSED SENSING THEORY
    Yang, Yimei
    Yang, Yujun
    2014 11TH INTERNATIONAL COMPUTER CONFERENCE ON WAVELET ACTIVE MEDIA TECHNOLOGY AND INFORMATION PROCESSING (ICCWAMTIP), 2014, : 196 - 199
  • [33] RADAR DETECTION METHOD BASED ON COMPRESSED SENSING THEORY
    Wang, Tianyun
    Liu, Bing
    Wei, Qiang
    Cong, Bo
    Kang, Kai
    PROCEEDINGS OF 2018 14TH IEEE INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING (ICSP), 2018, : 789 - 792
  • [34] IMAGE FUSION AND RECOGNITION BASED ON COMPRESSED SENSING THEORY
    Bai, Qiuchan
    Jin, Chunxia
    INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, 2015, 8 (01) : 159 - 180
  • [35] The Study of Image Reconstruction Based on Compressed Sensing Theory
    Fang, Min
    Liu, Yi-min
    Liu, Wan
    Chen, Hui
    NUMBERS, INTELLIGENCE, MANUFACTURING TECHNOLOGY AND MACHINERY AUTOMATION, 2012, 127 : 32 - +
  • [36] Application of Compressed Sensing Theory to Radar Signal Processing
    Zhu Lei
    Qiu Chunting
    PROCEEDINGS OF 2010 3RD IEEE INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND INFORMATION TECHNOLOGY (ICCSIT 2010), VOL 6, 2010, : 315 - 318
  • [37] SAL imaging algorithm based on compressed sensing theory
    He J.
    Zhang Q.
    Yang X.-Y.
    Luo Y.
    Zhang H.
    Zhu X.-P.
    Yuhang Xuebao/Journal of Astronautics, 2011, 32 (11): : 2395 - 2402
  • [38] On the Role of Sparsity in Compressed Sensing and Random Matrix Theory
    Vershynin, Roman
    2009 3RD IEEE INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP), 2009, : 189 - 192
  • [39] On the Role of Sparsity in Compressed Sensing and Random Matrix Theory
    Vershynin, Roman
    2009 3RD IEEE INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP 2009), 2009, : 189 - 192
  • [40] Classification of agricultural pests based on compressed sensing theory
    Han A.
    Guo X.
    Liao Z.
    Chen Z.
    Han J.
    Nongye Gongcheng Xuebao/Transactions of the Chinese Society of Agricultural Engineering, 2011, 27 (06): : 203 - 207
12345