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Block Sparse Signals Recovery via Block Backtracking-Based Matching Pursuit Method

  • Qi, Rui (School of Mathematics and Physics, China University of Geosciences) ;
  • Zhang, Yujie (School of Mathematics and Physics, China University of Geosciences) ;
  • Li, Hongwei (School of Mathematics and Physics, China University of Geosciences)
  • Received : 2015.10.28
  • Accepted : 2016.12.30
  • Published : 2017.04.30

Abstract

In this paper, a new iterative algorithm for reconstructing block sparse signals, called block backtracking-based adaptive orthogonal matching pursuit (BBAOMP) method, is proposed. Compared with existing methods, the BBAOMP method can bring some flexibility between computational complexity and reconstruction property by using the backtracking step. Another outstanding advantage of BBAOMP algorithm is that it can be done without another information of signal sparsity. Several experiments illustrate that the BBAOMP algorithm occupies certain superiority in terms of probability of exact reconstruction and running time.

Keywords

References

  1. D. L. Donoho, "For most large underdetermined systems of linear equations, the minimum $\ell_{1}$‐norm solution is also the sparsest solution," Communications on Pure and Applied Mathematics, vol. 59, no. 6, pp. 797-829, 2006. https://doi.org/10.1002/cpa.20132
  2. Y. H. Zhong, Z. Y. Huang, B. Zhu, and H. Wu, "Sparse channel estimation of single carrier frequency division multiple access based on compressive sensing," Journal of Information Processing Systems, vol. 11, no. 3, pp. 342-353, 2015. https://doi.org/10.3745/JIPS.03.0028
  3. F. Parvaresh, H. Vikalo, S. Misra, and B. Hassibi, "Recovering sparse signals using sparse measurement matrices in compressed DNA microarrays," IEEE Journal of Selected Topics in Signal Processing, vol. 2, no. 3, pp. 275-285, 2008. https://doi.org/10.1109/JSTSP.2008.924384
  4. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489-509, 2006. https://doi.org/10.1109/TIT.2005.862083
  5. E. Candes and T. Tao, "Decoding by linear programming," IEEE Transactions on Information Theory, vol. 51, no. 2, pp. 4203-4215, 2005. https://doi.org/10.1109/TIT.2005.858979
  6. D. L. Donoho, "Compressed sensing," IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289-1306, 2006. https://doi.org/10.1109/TIT.2006.871582
  7. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Journal on Scientific Computing, vol. 20, no. 1, pp. 33-61, 1998. https://doi.org/10.1137/S1064827596304010
  8. J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Transactions on Information Theory, vol. 53, no. 12, pp. 4655-4666, 2007. https://doi.org/10.1109/TIT.2007.909108
  9. D. L. Donoho, Y. Tsaig, I. Drori, and J. L. Starck, "Sparse solutions of underdetermined linear equations by stagewise orthogonal matching pursuit," IEEE Transactions on Information Theory, vol. 58, no. 2, pp. 1094- 1120, 2012. https://doi.org/10.1109/TIT.2011.2173241
  10. D. Needell and R. Vershynin, "Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit," Foundations of Computational Mathematics, vol. 9, no. 3, pp. 317-334, 2009. https://doi.org/10.1007/s10208-008-9031-3
  11. D. Needell and J. A. Tropp, "CoSaMP: iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harmonic Analysis, vol. 26, no. 3, pp. 301-321, 2009. https://doi.org/10.1016/j.acha.2008.07.002
  12. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Transactions on Information Theory, vol. 55, no. 5, pp. 2230-2249, 2009. https://doi.org/10.1109/TIT.2009.2016006
  13. H. Huang and A. Makur, "Backtracking-based matching pursuit method for sparse signal reconstruction," IEEE Signal Processing Letters, vol. 18, no. 7, pp. 391-394, 2011. https://doi.org/10.1109/LSP.2011.2147313
  14. H. Mohimani, M. Babaie-Zadeh, and C. Jutten. "A fast approach for overcomplete sparse decomposition based on smoothed l0-norm," IEEE Transactions on Signal Processing, vol. 57, no. 1, pp. 289-301, 2009. https://doi.org/10.1109/TSP.2008.2007606
  15. Y. C. Eldar and P. Kuppinger, "Block-sparse signals: uncertainty relations and efficient recovery," IEEE Transactions on Signal Processing, vol. 58, no. 6, pp. 3042-3054, 2010. https://doi.org/10.1109/TSP.2010.2044837
  16. M. Mishali and Y. C. Eldar, "Blind multi-band signal reconstruction: compressed sensing for analog signals," IEEE Transaction on Signal Processing, vol. 57, no. 3, pp. 993-1009, 2009. https://doi.org/10.1109/TSP.2009.2012791
  17. S. F. Cotter and B. D. Rao, "Sparse channel estimation via matching pursuit with application to equalization," IEEE Transactions on Communication, vol. 50, no. 3, pp. 374-377, 2002. https://doi.org/10.1109/26.990897
  18. Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Transactions on Information Theory, vol. 55, no. 11, pp. 5302-5316, 2009. https://doi.org/10.1109/TIT.2009.2030471
  19. Z. Zeinalkhani and A. H. Banihashemi, ''Iterative reweighted l2/l1 recovery algorithms for compressed sensing of block sparse signals," IEEE Transactions on Signal Processing, vol. 63, no. 17, pp. 4516-4531, 2015. https://doi.org/10.1109/TSP.2015.2441032
  20. S. Hamidi-Ghalehjegh, M. Babaie-Zadeh, and C. Jutten, "Fast block-sparse decomposition based on SL0," in Proceedings of 9th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA), St. Malo, France, 2010, pp. 426-433.
  21. R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Transactions on Communication, vol. 56, no. 4, pp. 1982-2001, 2010.
  22. B. X. Huang and T. Zhou, "Recovery of block sparse signals by a block version of StOMP," Signal Processing, vol. 106, pp. 231-244, 2015. https://doi.org/10.1016/j.sigpro.2014.07.023
  23. Y. Wang, J, Wang, and Z. Xu, "On recovery of block-sparse signals via mixed $\ell_{2}/\ell_{q}$ ($0) norm minimization," EURASIP Journal on Advances in Signal Processing, vol. 2013, article no. 76, pp. 1-17, 2013. https://doi.org/10.1186/1687-6180-2013-1
  24. H. Yin, S. Li, and L. Fang, "Block-sparse compressed sensing: non-convex model and iterative re-weighted algorithm," Inverse Problems in Science and Engineering, vol. 21, no. 1, pp. 141-154, 2013. https://doi.org/10.1080/17415977.2012.677444