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Adaptive Step-Size Matching Pursuit Algorithm for Practical Sparse Reconstruction

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Abstract

A novel adaptive step-size matching pursuit algorithm (AStMP) is proposed. AStMP reduces the computational cost and increases the accuracy of reconstructing practical signals (i) whose sparsity K is unknown and/or (ii) may be corrupted by noise. AStMP accurately estimates K by combining the sparsity estimate of sparsity adaptive subspace pursuit (SASP) with the adaptively changing stepsize at each stage of sparsity adaptive matching pursuit (SAMP). Thus, AStMP can quickly achieve accurate estimation of the sparsity level and the true support set of the target signals. Meanwhile, a preselection is employed to reduce the computational complexity of each stage. When K is greater than half the number of measurements M, the probability of exact recovery is improved by analyzing the support set. Since the stepsize changes adaptively, AStMP can be applied in both the noiseless and noisy cases when the signal is not strictly sparse, allowing for exact or approximate signal recovery. Experimental results demonstrate that the AStMP is effective in fast and exact reconstruction and has good performance.

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References

  1. T. Blumensath, M.E. Davies, Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265–274 (2009). doi:10.1016/j.acha.2009.04.002

    Article  MathSciNet  MATH  Google Scholar 

  2. C.R. Berger, Z. Wang, J. Huang et al., Application of compressive sensing to sparse channel estimation. IEEE Commun. Mag. 48(11), 164–174 (2010). doi:10.1109/MCOM.2010.5621984

    Article  Google Scholar 

  3. S.S. Chen, D.L. Donoho, M.A. Saunders, Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20(1), 33–61 (1998). doi:10.1137/S1064827596304010

    Article  MathSciNet  MATH  Google Scholar 

  4. E.J. Candès, J.K. Romberg, T. Tao, Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure. Appl. Math. 59(8), 1207–1223 (2006). doi:10.1002/cpa.20124

    Article  MathSciNet  MATH  Google Scholar 

  5. E.J. Candès, J.K. Romberg, T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006). doi:10.1109/TIT.2005.862083

    Article  MathSciNet  MATH  Google Scholar 

  6. E.J. Candès, T. Tao, Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005). doi:10.1109/TIT.2005.858979

    Article  MathSciNet  MATH  Google Scholar 

  7. D.L. Donoho, Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006). doi:10.1109/TIT.2006.871582

    Article  MathSciNet  MATH  Google Scholar 

  8. T. T. Do, G. Lu, N. Nguyen, T. D. Tran, Sparsity adaptive matching pursuit algorithm for practical compressed sensing. In: Proceedings of the 42nd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California. pp. 581–587 (2008). doi:10.1109/ACSSC.2008.5074472

  9. D.L. Donoho, Y. Tsaig, Jean-Luc Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit. IEEE Trans. Inf. Theory 58(2), 1094–1121 (2006). doi:10.1109/TIT.2011.2173241

    Article  MathSciNet  Google Scholar 

  10. J. E. Fowler, Compressive pushbroom and whiskbroom sensing For hyperspectral remote-sensing imaging. Image Processing (ICIP), In: 2014 IEEE International Conference. 684–688 (2014). doi:10.1109/ICIP.2014.7025137

  11. M.A.T. Figueiredo, R.D. Nowak, S.J. Wright, Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007). doi:10.1109/JSTSP.2007.910281

    Article  Google Scholar 

  12. H. Fang, H. Yang, A new compressed sensing-based matching pursuit algorithm for image reconstruction. In: International Congress on Image and Signal Processing (CISP). pp. 338–342 (2012). doi:10.1109/CISP.2012.6469673

  13. Ioannis Kyriakides, Adaptive compressive sensing and processing of Delay–Doppler radar waveforms. IEEE Trans. Signal Process. 60(2), 730–739 (2012). doi:10.1109/TSP.2011.2174234

    Article  MathSciNet  Google Scholar 

  14. L.B. Montefusco, D. Lazzaro, S. Papi, C. Guerrini, A fast compressed sensing approach to 3D MR image reconstruction. IEEE Trans. Med. Imaging 30(5), 1064–1075 (2011). doi:10.1109/TMI.2010.2068306

    Article  Google Scholar 

  15. D. Needell, J.A. Tropp, CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2008). doi:10.1016/j.acha.2008.07.002

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Needell, R. Vershynin, Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. IEEE J. Sel. Top. Signal Process. 4(2), 310–316 (2007). doi:10.1109/JSTSP.2010.2042412

    Article  Google Scholar 

  17. D. Ramasamy, S. Venkateswaran, U. Madhow, Compressive parameter estimation in AWGN. IEEE Trans. Signal Process. 62(8), 2012–2027 (2014). doi:10.1109/TSP.2014.2306180

    Article  MathSciNet  Google Scholar 

  18. J. Tropp, A. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007). doi:10.1109/TIT.2007.909108

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Wang, Z. Lu, Y. Li, A. New, CDMA encoding/decoding method for on-chip communication network. IEEE Trans. Very Larg Scale Integr. (VLSI) Syst. 24(4), 1607–1611 (2015). doi:10.1109/TVLSI.2015.2471077

    Article  Google Scholar 

  20. D. Wei, O. Milenkovic, Subspace pursuit for compressive sensing: closing the gap between performance and complexity. Technical Report, arXiv:0803.0811 (2008). http://cds.cern.ch/record/1093014

  21. C. Yang, W. Feng, H. Feng et al., A sparsity adaptive subspace pursuit algorithm for compressive sampling. Acta Electron. Sin. (in Chinese). 38(4), 1914–1917 (2010)

    Google Scholar 

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Authors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Yusheng Fu, Shanshan Liu & Chunhui Ren

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  1. Yusheng Fu
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  2. Shanshan Liu
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  3. Chunhui Ren
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Correspondence to Yusheng Fu.

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Fu, Y., Liu, S. & Ren, C. Adaptive Step-Size Matching Pursuit Algorithm for Practical Sparse Reconstruction. Circuits Syst Signal Process 36, 2275–2291 (2017). https://doi.org/10.1007/s00034-016-0393-5

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  • DOI: https://doi.org/10.1007/s00034-016-0393-5

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