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Efficient Parameters for Compressed Sensing Recovery Algorithms

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Abstract

Compressed sensing CS has been an effective research area which it plays an efficient role in many applications such as cognitive radio, imaging, radar and many other applications. The main part of CS system is to recover an input signal by using minimum number of samples than used by conventional (Nyquist) sampling. In this paper, the minimum number of measurements and the number of sparsity level used to reconstruct the signal with minimum error, computational complexity and time will be optimized. Moreover, different recovery algorithms such as convex optimization, greedy algorithms, iterative hard thresholding and hard thresholding pursuit algorithms are used for optimal recovery of sparse signal from a small number of linear measurements. Furthermore, the effect of using CS as denosing will be investigated. Then comparisons study between CS as denoising and conventional denoising process will be made to reduce the effect of noise on the signal.

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References

  1. Dohoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52, 1289–1306.

    Article  MathSciNet  MATH  Google Scholar 

  2. Shannon, C. E. (1949). Communication in the presence of noise. Proceedings of the IRE, 37(1), 10–21.

    Article  MathSciNet  Google Scholar 

  3. Mishali, M., & Eldar, Y. (2010). From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals. IEEE Journal of Selected Topics in Signal Processing, 4(2), 375–391.

    Article  Google Scholar 

  4. Desai, S., & Nakrani, N. (2013). Compressive sensing in speech processing: A survey based on sparsity and sensing matrix. International Journal of Emerging Technology and Advanced Engineering, 3(12), 18–23.

    Google Scholar 

  5. Rudelson, M., & Vershynin, R. (2008). On sparse reconstruction from Fourier and Gaussian measurements. Communications on Pure and Applied Mathematics, 61, 1025–1045.

    Article  MathSciNet  MATH  Google Scholar 

  6. Boyd, S. P., & Vandenberghe, L. (2004). Convex optimization. Cambridge: Cambridge Univ Press.

    Book  MATH  Google Scholar 

  7. Candes, E., & Ta, T. (2005). Decoding by linear programming. IEEE Transactions on Information Theory, 40698, 1–22.

    MathSciNet  Google Scholar 

  8. Mallat, S. G., & Zhang, Z. (1993). Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41(12), 3397–3415.

    Article  MATH  Google Scholar 

  9. DeVore, R. A., & Temlyakov, V. N. (1996). Some remarks on greedy algorithms. Advances in Computational Mathematics, 5, 173–187.

    Article  MathSciNet  MATH  Google Scholar 

  10. Needell, D., & Tropp, J. A. (2008). COsaMP: Iterative signal recovery for incomplete and in accurate sample. Applied and Computional Harmonic analysis, 26(3), 301–321.

    Article  MATH  Google Scholar 

  11. Blvmensath, T., & Davies, M. (2009). Iterative hard thresholding for compressed sensing. Applied and Computational Harmonic Analysis, 27(3), 265–274.

    Article  MathSciNet  MATH  Google Scholar 

  12. Blumensath, T., & Davies, M. E. (2010). Normalized iterative hard thresholding: Guaranteed stability and performance. IEEE Journal of Selected Topics in Signal Processing, 4(2), 298–309.

    Article  Google Scholar 

  13. Somon FouCART. (2011). Hard thresholding pursuit: An algorithm for compressive sensing. SIAM Journal on Numerical Analysis, 49(6), 2543–2563.

    Article  MathSciNet  MATH  Google Scholar 

  14. Hayashi, K., Nagahara, N., & Tanaka, T. (2013). A user’s guide to compressed sensing for communication system. IEICE Transactions on Communications, 96(3), 685–712.

    Article  Google Scholar 

  15. Kutyniok, G. (2012). Compressed sensing theory and application. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  16. Gribonval, R., & Nielsen, M. (2003). Sparse representations in unions of bases. IEEE Transactions on Information Theory, 49(12), 3320–3325.

    Article  MathSciNet  MATH  Google Scholar 

  17. Welch, L. R. (1974). Lower bounds on the maximum cross correlation of signals. IEEE Transactions on Information Theory, 20(3), 397–399.

    Article  MATH  Google Scholar 

  18. Donoho, D. L., & Elad, M. (2003). Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ 1 minimization. Proceedings of the National Academy of Sciences, 100(5), 2197–2202.

    Article  MathSciNet  MATH  Google Scholar 

  19. Candès, E. J. (2006). Compressive sampling. In Proceedings of international congress of mathematicians (Vol. 3, pp. 1433–1452). Madrid, Spain.

  20. Cai, T. T., Xu, G., & Zhang, J. (2009). On recovery of sparse signals via ℓ 1 minimization. IEEE Transactions on Information Theory, 55(7), 3388–3397.

    Article  MathSciNet  Google Scholar 

  21. DeVore, R. A. (2007). Deterministic constructions of compressed sensing matrices. Journal of Complexity, 23(4), 918–925.

    Article  MathSciNet  MATH  Google Scholar 

  22. Donoho, D. (2006). For most large underdetermined systems of linear equations, the minimal ℓ 1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 59(6), 797–829.

    Article  MathSciNet  MATH  Google Scholar 

  23. Candès, E. J., & Plan, Y. (2009). Near-ideal model selection by ℓ 1 minimization. Annals of Statistics, 37(5A), 2145–2177.

    Article  MathSciNet  MATH  Google Scholar 

  24. Baraniuk, R. G., Davenport, M., DeVore, R., & Wakin, M. (2008). A simple proof of the restricted isometry property for random matrices. Constructive Approximation, 28(3), 253–263.

    Article  MathSciNet  MATH  Google Scholar 

  25. Rockafellar, R. T. (1970). Convex analysis. Princeton: Princeton University Press.

    Book  MATH  Google Scholar 

  26. Candes, E., & Romberg, J. (2005). L1-MAGIC: Recovery of sparse signals via convex programming. Techical Report, Caltech.

  27. Donoho, D., Tsaig, Y., Drori, I., & Starck, J. (2012). Sparse solution of underdetermined system of linear equations by stagewise orthogonal matching pursuit. IEEE Transactions on Information Theory, 58(2), 1094–1121.

    Article  MathSciNet  Google Scholar 

  28. Needell, D., & Vreshynin, R. (2009). Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Foundations of Computational Mathematics, 9(3), 317–334.

    Article  MathSciNet  MATH  Google Scholar 

  29. Patil, P. B., & Chavan, M. S. (2012). A wavelet based method for denoising of biomedical signal. In Proceedings of the international conference on pattern recognition, informatics and medical engineering, March 21–23.

  30. Tavakoli, A., & Pourmohammad, A. (2012). Image denoising based on compressed sensing. International Journal of Computer Theory and Engineering, 4, 266–269.

  31. Wan-zheng, N., Hai-yan, W., Xuan, W., & Fu-zhou, Y. (2011). The analysis of noise reduction performance in compressed sensing. In IEEE international conference on signal processing, communications and computing (ICSPCC) (Vol. 1, No. 5, pp. 14–16).

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Authors and Affiliations

  1. Electrical and Electronic Communication Engineering Department, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt

    Wafaa A. Shalaby, Waleed Saad, Mona Shokair & Moawad Dessouky

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  1. Wafaa A. Shalaby
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  2. Waleed Saad
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  3. Mona Shokair
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  4. Moawad Dessouky
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Correspondence to Wafaa A. Shalaby.

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Shalaby, W.A., Saad, W., Shokair, M. et al. Efficient Parameters for Compressed Sensing Recovery Algorithms. Wireless Pers Commun 94, 1715–1736 (2017). https://doi.org/10.1007/s11277-016-3708-8

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  • DOI: https://doi.org/10.1007/s11277-016-3708-8

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