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Circuits, Systems, and Signal Processing

, Volume 38, Issue 2, pp 918–929 | Cite as

Preprocessed Compressive Adaptive Sense and Search Algorithm

  • Yun LinEmail author
  • Qiang Hu
Short Paper
  • 41 Downloads

Abstract

To address the performance degradation due to the cancellation of positive and negative entries of adaptive compressed sensing algorithms, we propose a simple adaptive sensing and group testing algorithm for sparse signals. The algorithm, termed “preprocessed compressive adaptive sense and search”, divides the input signal into two equal-length subsignals that include only non-positive or non-negative entries through a nonlinear preprocessing process and subsequently generates adaptive sensing and group testing. The proposed algorithm is computationally less intensive than non-adaptive compressed sensing and requires only klog(n/k) measurements to recover a k-sparse signal of dimension n. A theoretical guarantee for signal recovery is provided, and the provided numerical examples demonstrate a better recovery performance than non-adaptive sensing and compressive adaptive sense and search algorithms for the same signal-to-noise ratio.

Keywords

Compressed sensing Adaptive measurement Sparse Preprocessing CASS 

References

  1. 1.
    E. Arias-Castro, Y.C. Eldar, Noise folding in compressed sensing. IEEE Signal Process. Lett. 18(6), 478–481 (2011)CrossRefGoogle Scholar
  2. 2.
    E. Arias-Castro, E. Candes, M. Davenport, On the fundamental limits of adaptive sensing. IEEE Trans. Inf. Theory 59(1), 472–481 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    E. Bashan, G. Newstadt, A.O. Hero, Two-stage multiscale search for sparse targets. IEEE Trans. Signal Process. 59(5), 2331–2341 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    G. Braun, S. Pokutta, Y. Xie, Info-Greedy sequential adaptive compressed sensing. IEEE J. Sel. Topics Signal Process. 9(4), 601–611 (2015)CrossRefGoogle Scholar
  5. 5.
    E.J. Candès, T. Tao, Near-optimal signal recovery from random projections. Universal encoding strategies. IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    M.A. Davenport, E. Arias-Castro, Compressive binary search, pp. 1827–1831 (2012)Google Scholar
  7. 7.
    M. Davenport, A. Massimino, D. Needell, T. Woolf, Constrained adaptive sensing. IEEE Trans. Signal Process. 64(10), 5437–5449 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    D. Donoho, Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Y.C. Eldar, G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University Press, Cambridge, 2012)CrossRefGoogle Scholar
  10. 10.
    J. Haupt, R. Baraniuk, R. Castro, R. Nowak, Sequentially designed compressed sensing. In: Proceedings IEEE/SP Workshop Statistics Signal Process, pp. 401–404 (2012)Google Scholar
  11. 11.
    S. Ji, Y. Xue, L. Carin, Bayesian compressive sensing. IEEE Trans. Signal Process. 56(6), 2346–2356 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    D. Malioutov, S. Sanghavi, A. Willsky, Sequential compressed sensing. IEEE J. Sel. Topics Signal Process. 4(2), 435–444 (2010)CrossRefGoogle Scholar
  13. 13.
    M.L. Malloy, R. Nowak, Near-optimal adaptive compressed sensing. IEEE Trans. Inf. Theory 60(7), 4001–4012 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    A. Tajer, R.M. Castro, X. Wang, Adaptive sensing of congested spectrum bands. IEEE Trans. Inf. Theory 58(9), 6110–6125 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    S.J. Wright, R.D. Nowak, M.A. Figueiredo, Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 2479–2493 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    S. Zehetmayer, P. Bauer, M. Posch, Optimized multi-stage designs controlling the false discovery or the family-wise error rate. Stat. Med. 27, 4145–4160 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chongqing Key Lab of Mobile Communications TechnologyChongqing University of Posts and TelecommunicationsChongqingPeople’s Republic of China

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