Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Sparse Signal Recovery via Tree Search Matching Pursuit

  • Lee, Jaeseok (Dept. of Information and Communication Engineering, Daegu Gyeongbuk Institute of Science and Technology) ;
  • Choi, Jun Won (Dept. of Electrical Engineering, Hanyang University) ;
  • Shim, Byonghyo (Institute of New Media and Communications and School of Electrical and Computer Engineering, Seoul National University)
  • Received : 2016.08.16
  • Published : 2016.10.31
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Abstract

Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the support (index set of nonzero elements) of the sparse signals. Well-known drawback of the greedy approach is that the chosen candidate is often not the optimal solution due to the myopic decision in each iteration. In this paper, we propose a tree search based sparse signal recovery algorithm referred to as the tree search matching pursuit (TSMP). Two key ingredients of the proposed TSMP algorithm to control the computational complexity are the pre-selection to put a restriction on columns of the sensing matrix to be investigated and the tree pruning to eliminate unpromising paths from the search tree. In numerical simulations of Internet of Things (IoT) environments, it is shown that TSMP outperforms conventional schemes by a large margin.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  1. E. J. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006. https://doi.org/10.1109/TIT.2005.862083
  2. E. J. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005, https://doi.org/10.1109/TIT.2005.858979
  3. E. Liu and V. N. Temlyakov, "The orthogonal super greedy algorithm and applications in compressed sensing," IEEE Trans. Inf. Theory, vol. 58, no. 4, pp. 2040-2047, Apr. 2012. https://doi.org/10.1109/TIT.2011.2177632
  4. E. J. Candes, "The restricted isometry property and its implications for compressed sensing," Comptes Rendus Mathematique, vol. 346, no. 9-10, pp. 589-592, May 2008. https://doi.org/10.1016/j.crma.2008.03.014
  5. R. Tibshirani, "Regression shrinkage and selection via the Lasso," J. Royal Stat. Soc. Series B, vol. 58, no. 1, pp. 267-288, 1996.
  6. E. J. Candes and T. Tao, "The dantzig selector: statistical estimation when p is much larger than n," The Annal. Stat., vol. 35, no. 6, pp. 2313-2351, Dec. 2007. https://doi.org/10.1214/009053606000001523
  7. T. T. Cai and L. Wang, "Orthogonal matching pursuit for sparse signal recovery with noise," IEEE Trans. Inf. Theory, vol. 57, no. 7, pp. 4680-4688, July 2011. https://doi.org/10.1109/TIT.2011.2146090
  8. J. Wang and B. Shim, "On the recovery limit of sparse signals using orthogonal matching pursuit," IEEE Trans. Signal Process., vol. 60, no. 9, pp. 4973-4976, Sept. 2012. https://doi.org/10.1109/TSP.2012.2203124
  9. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," ACM Commun., vol. 53, no. 12, pp. 93-100, Dec. 2010.
  10. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. Inf. Theory, vol. 55, no. 5, pp. 2230-2249, May 2009. https://doi.org/10.1109/TIT.2009.2016006
  11. T. Blumensath and M. E. Davies, "Iterative hard thresholding for compressed sensing," Applied and Computational Harmonic Analysis, vol. 27, no. 3, pp. 265-274, Nov. 2009. https://doi.org/10.1016/j.acha.2009.04.002
  12. R. Garg and R. Khandekar, "Gradient descent with sparsification: An iterative algorithm for sparse recovery with restricted isometry property," in Proc. Annual International Conf. Machine Learning, pp. 337-344, May 2009.
  13. S. Foucart, "Hard thresholding pursuit: An algorithm for compressive sensing," SIAM J. Numerical Analysis, vol. 49, no. 6, pp. 2543-2563, Dec. 2011. https://doi.org/10.1137/100806278
  14. M. A. Khajehnejad, A. G. Dimakis, W. Xu, and B. Hassibi, "Sparse recovery of nonnegative signals with minimal expansion," IEEE Trans. Signal Process., vol. 59, no. 1, pp. 196-208, Jan. 2011. https://doi.org/10.1109/TSP.2010.2082536
  15. S. Qaisar, R. M. Bilal, W. Iqbal, M. Naureen, and S. Lee, "Compressive sensing: From theory to applications, a survey," J. Commun. Netw., vol. 15, no. 5, pp. 443-456, Oct. 2013. https://doi.org/10.1109/JCN.2013.000083
  16. S. Kwon, J. Wang, and B. Shim, "Multipath matching pursuit," IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 4867-4878, Oct. 2013.
  17. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Scientific Comput., pp. 33-61, 1998.
  18. W. Chen, M. R. D. Rodrigues, I. J. Wassell, and L. Hanzo, "Projection design for statistical compressive sensing: A tight frame based approach," IEEE Trans. Signal Process., vol. 61, no. 8, pp. 2016-2029, April 2013. https://doi.org/10.1109/TSP.2013.2245661
  19. T. Zhang, "Sparse recovery with orthogonal matching pursuit under RIP," IEEE Trans. Inf. Theory, vol. 57, no. 9, pp. 6215-6221, Sept. 2011. https://doi.org/10.1109/TIT.2011.2162263
  20. J. Wang, S. Kwon, and B. Shim, "Generalized orthogonal matching pursuit," IEEE Trans. Signal Process., vol. 60, no. 12, pp. 6202-6216, Dec. 2012. https://doi.org/10.1109/TSP.2012.2218810
  21. G. D. Forney Jr., "The Viterbi algorithm," in Proc. IEEE, pp. 268-278, Mar. 1973.
  22. E. Viterbo and J. Boutros, "A universal lattice code decoder for fading channels," IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1639-1642, July 1999. https://doi.org/10.1109/18.771234
  23. B. Shim and I. Kang, "Sphere decoding with a probabilistic tree pruning," IEEE Trans. Signal Process., vol. 56, no. 10, pp. 4867-4878, Oct. 2008. https://doi.org/10.1109/TSP.2008.923808
  24. J. Choi, B. Lee and B. Shim, "Iterative group detection and decoding for large MIMO systems," J. Commun. and Netw., vol 17. pp. 609-621, Dec. 2015. https://doi.org/10.1109/JCN.2015.000108