Infrared Image Reconstruction Based on Archimedes Spiral Measurement Matrix

  • Yilin Jiang (蒋伊琳)Email author
  • Haiyan Wang (王海艳)
  • Ran Shao (邵然)
  • Jianfeng Zhang (张建峰)


It is a new research direction to realize infrared (IR) image reconstruction using compressed sensing (CS) theory. In the field of CS, the construction of measurement matrix is very principal. At present, the types of measurement matrices are mainly random and deterministic. The random measurement matrix can well satisfy the property of measurement matrix, but needs a large amount of storage space and has an inconvenient in hardware implementation. Therefore, a deterministic measurement matrix construction method is proposed for IR image reconstruction in this paper. Firstly, a series of points are collected on Archimedes spiral to construct a definite sequence; then the initial measurement matrix is constructed; finally, the deterministic measurement matrix is obtained according to the required sampling rate. Simulation results show that the IR image could be reconstructed by the measured values obtained through the proposed measurement matrix. Moreover, the proposed measurement matrix has better reconstruction performance compared with the Gaussian and Bernoulli random measurement matrices.

Key words

compressed sensing (CS) infrared image reconstruction deterministic measurement matrices 

CLC number

TN 911.73 

Document code


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    ZHOU M H, CHEN Q. Advances in medical infrared thermal imaging technology [J]. Infrared, 2008, 29(2): 38–42 (in Chinese).Google Scholar
  2. [2]
    SHAO J, HU W Y, JIA F M, et al. Application of infrared thermal imaging technology to condition-based maintenance of power equipment [J]. High Voltage Apparatus, 2013, 49(1): 126–129 (in Chinese).Google Scholar
  3. [3]
    MARSHALL M V, RASMUSSEN J C, TAN I, et al. Near-infrared fluorescence imaging in humans with indocyanine green: A review and update [J]. Open Surgical Oncology Journal, 2010, 2(2): 12–25.CrossRefGoogle Scholar
  4. [4]
    CANDES E J, TAO T. Decoding by linear programming [J]. IEEE Transactions on Information Theory, 2005, 51(12): 4203–4215.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    DONOHO D L. Compressed Sensing [J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    DUARTE M F, DAVENPORT M A, TAKHAR D, et al. Single-pixel imaging via compressive sampling [J]. IEEE Signal Processing Magazine, 2008, 25(2): 83–91.CrossRefGoogle Scholar
  7. [7]
    ZHANG M, BERMAK A. Compressive acquisition CMOS image sensor: From the algorithm to hardware implementation [J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2010, 18(6): 490–500.CrossRefGoogle Scholar
  8. [8]
    YANG A Y. GASTPAR M, BAJCSY R, et al. Distributed sensor perception via sparse representation [J]. Proceedings of the IEEE, 2010, 98(9): 1077–1088.Google Scholar
  9. [9]
    DAVENPORT M A, WAKIN M B. Analysis of orthogonal matching pursuit using the restricted isometry property [J]. IEEE Transactions on Information Theory, 2010, 56(9): 4395–4401.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    TSAIG Y, DONOHO D L. Extensions of compressed sensing [J]. Signal Processing, 2006, 86(3): 549–571.CrossRefzbMATHGoogle Scholar
  11. [11]
    XIE C J, LIN X, ZHANG T S. Research of image reconstruction of compressed sensing using basis pursuit algorithm [J]. Electronic Design Engineering, 2011, 19(11): 163–166 (in Chinese).Google Scholar
  12. [12]
    CHEN S, DONOHO D L, SAUNDERS M A. Atomic decomposition by basis pursuit [J]. SIAM Journal on Scientific Computing, 1998, 20(1): 33–61.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    TROPP J A, GILBERT A C. Signal recovery from random measurements via orthogonal matching pursuit [J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655–4666.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    DONOHO D L, TSAIG Y, DRORI I, et al. Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit [J]. IEEE Transactions on Information Theory, 2012, 58(2): 1094–1121.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    WANG Q, LI J, SHEN Y. A survey on deterministic measurement matrix construction algorithms in compressive sensing [J]. Acta Electronica Sinica, 2013, 41(10): 2041–2050 (in Chinese).Google Scholar
  16. [16]
    YU Y, PETROPULU A P, POOR H V. Measurement matrix design for compressive sensing–based MIMO radar [J]. IEEE Transactions on Signal Processing, 2011, 59(11): 5338–5352.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    ZHANG G, JIAO S, XU X, et al. Compressed sensing and reconstruction with Bernoulli matrices [C]//IEEE International Conference on Information and Automation. Harbin, China: IEEE, 2010: 455–460.Google Scholar
  18. [18]
    DEVORE R A. Deterministic constructions of Compressed sensing matrices [J]. Journal of Complexity, 2007, 23(4/5/6): 918–925.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    ZHAO R Z, WANG R Q, ZHANG F Z, et al. Research on the blocked ordered Vandermonde matrix used as measurement matrix for compressed sensing [J]. Journal of Electronics & Information Technology, 2015, 37(6): 1317–1322 (in Chinese).Google Scholar
  20. [20]
    SUN R, ZHAO H, XU H. The application of improved Hadamard measurement matrix in compressed sensing [C]//International Conference on Systems and Informatics. Yantai, China: IEEE, 2012: 1994–1997.Google Scholar
  21. [21]
    YU N Y, LI Y. Deterministic construction of Fourierbased compressed sensing matrices using an almost difference set [J]. EURASIP Journal on Advances in Signal Processing, 2013(1): 1–14.Google Scholar
  22. [22]
    BAJWA W U, HAUPT J D, RAZ G M, et al. Toeplitz-structured compressed sensing matrices [C]//Workshop on Statistical Signal Processing. Madison, WI, USA: IEEE, 2007: 294–298.Google Scholar
  23. [23]
    YIN W. Practical compressive sensing with Toeplitz and circulant matrices [EB/OL]. [2017-11-16]. Practical Compressive Sensing with Toeplitz and Circulant Matrices.Google Scholar
  24. [24]
    LU W, LI W, KPALMA K, et al. Compressed sensing performance of random Bernoulli matrices with high compression ratio [J]. IEEE Signal Processing Letters, 2015, 22(8): 1074–1078.CrossRefGoogle Scholar
  25. [25]
    SHI G M, LIU D H, GAO D H, et al. Advances in theory and application of compressed sensing [J]. Acta Electronica Sinica, 2009, 37(5): 1070–1081 (in Chinese).Google Scholar

Copyright information

© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yilin Jiang (蒋伊琳)
    • 1
    Email author
  • Haiyan Wang (王海艳)
    • 1
  • Ran Shao (邵然)
    • 1
  • Jianfeng Zhang (张建峰)
    • 1
  1. 1.College of Information and Communication EngineeringHarbin Engineering UniversityHarbinChina

Personalised recommendations