Abstract
In wireless sensor networks (WSNs), thousands of sensor nodes are deployed to measure various environmental parameters such as temperature, light intensity, humidity and air pressure. All living beings can sense the variation in these parameters; therefore, these parameters are termed as natural signals. The natural signals are highly correlated in time and space; therefore, it can be compressed significantly to achieve the low sampling rates. The correlation property of natural signals is exploited here to compress/decompress these signals for reducing the transmission cost of the networks. The real-time temperature signal is measured using national instruments (NI) WSN platform, which is used for analysis purpose. The signal at first is transformed into sparse signal and then compressed. The compressed signal is transmitted to the receiver, where it is decoded into original sparse signal using algorithms based on greedy iterative approaches, i.e. orthogonal matching pursuit (OMP), stagewise orthogonal matching pursuit (StOMP) and generalized OMP (gOMP). The most popular greedy algorithm, OMP, is compared with StOMP and gOMP. The performance is analysed quantitatively in terms of peak signal-to-noise ratio, root- mean-squared error and execution speed of these greedy algorithms. It is demonstrated through simulation, the computational speed of StOMP and gOMP is much better than OMP, and also, the sparse signal is recovered with accuracy approximately equal to OMP.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Needell, D.: Topics in compressed sensing. arXiv preprint arXiv:0905.4482 (2009)
Qaisar, S.; Bilal, R.M.; Iqbal, W.; Naureen, M.; Lee, S.: Compressive sensing: from theory to applications, a survey. J. Commun. Netw. 15(5), 443–456 (2013)
Breen, P.: Algorithms for sparse approximation. School of Mathematics, University of Edinburgh,4. (2009). https://s3.amazonaws.com/academia.edu.documents/42908668/file_5_52170211052012.pdf?AWSAccessKeyId=AKIAIWOWYYGZ2Y53UL3A&Expires=1504374516&Signature=pDMqbk%2BXS210FjqF3dGs7UcVHDQ%3D&response-content-disposition=inline%3B%20filename%3DAlgorithms_for_Sparse_Approximation.pdf
Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
Candès, E.J.; Wakin, M.B.: An introduction to compressive sampling. IEEE Signal Process. Mag. 25(2), 21–30 (2008)
Patterson, S.; Eldar, Y. C.; Keidar, I.: Distributed sparse signal recovery for sensor networks. In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4494–4498 (2013).
Akyildiz, I.F.; Su, W.; Sankarasubramaniam, Y.; Cayirci, E.: Wireless sensor networks: a survey. Comput. Netw. 38(4), 393–422 (2002)
Cheng, L.; Cao, J.; Chen, C.; Chen, H.; Ma, J.: Towards intelligent contention-based geographic forwarding in wireless sensor networks. IET Commun. 5(11), 1711–1719 (2011)
Huang, P.; Chen, H.; Xing, G.; Tan, Y.: SGF: a state-free gradient-based forwarding protocol for wireless sensor networks. ACM Trans. Sens. Netw. (TOSN) 5(2), 14 (2009)
Yue, Y.; Li, J.; Fan, H.; Qin, Q.: Optimization-based extreme learning machine for data fusion in mobile wireless sensor networks. Int. J. Innov. Comput. Inf. Control 12(5), 1423–1438 (2016)
Li, H.; Zhao, Y.; Sun, Y.: Wireless sensor network based on high-dimensional quantum communication. Int. J. Innov. Comput Inf. Control 11(6), 2119–2133 (2015)
Ravelomanantsoa, A.; Rabah, H.; Rouane, A.: Compressed sensing: A simple deterministic measurement matrix and a fast recovery algorithm. IEEE Trans. Instrum. Meas. 64(11), 3405–3413 (2015)
Ravelomanantsoa, A.; Rabah, H.; Rouane, A.: Fast and efficient signals recovery for deterministic compressive sensing: Applications to biosignals. In: 2015 Conference on Design and Architectures for Signal and Image Processing (DASIP), pp. 1–6 (2015)
Baraniuk, R.G.: Compressive sensing. IEEE Signal Process. Mag. 24(4), 118–121 (2007)
Davenport, M.A.; Duarte, M.F.; Eldar, Y.C.; Kutyniok, G.: Introduction to compressed sensing. In: Eldar, Y.C., Kutyniok, G. (eds.) Compressed Sensing: Theory and Applications, pp. 1–64. Cambridge University Press, Cambridge (2012)
Candes, E.J.; Romberg, J.K.; Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)
Tropp, J.A.: Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004)
Tropp, J.A.; Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(11), 4655–4666 (2007)
Donoho, D.L.; Tsaig, Y.; Drori, I.; Starck, J.-L.: Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012)
Dai, W.; Milenkovic, O.: Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans. Inf. Theory 55(5), 2230–2249 (2009)
Needell, D.; Tropp, J.A.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmonic Anal. 26(3), 301–321 (2009)
Pilastri, A. L.; Tavares, J. M.: Reconstruction algorithms in compressive sensing: an overview. In: 11th Edition of the Doctoral Symposium in Informatics Engineering (DSIE‘ 16) (2016)
Wang, J.; Kwon, S.; Shim, B.: Generalized orthogonal matching pursuit. IEEE Trans. Signal Process. 60(11), 6202–6216 (2012)
Liu, E.; Temlyakov, V.N.: The orthogonal super greedy algorithm and applications in compressed sensing. IEEE Trans. Inf. Theory 58(4), 2040–2047 (2012)
Xu, Z.: The performance of orthogonal multi-matching pursuit under the restricted isometry property. J. Comput. Math. 33(5), 495–516 (2015)
Sartipi, M.: Low-complexity distributed compression in wireless sensor networks. Data Compress. Conf. (DCC) 2012, 227–236 (2012)
Quer, G.; Masiero, R.; Pillonetto, G.; Rossi, M.; Zorzi, M.: Sensing, compression, and recovery for WSNs: sparse signal modeling and monitoring framework. IEEE Trans. Wireless Commun. 11(10), 3447–3461 (2012)
Razzaque, M.A.; Dobson, S.: Energy-efficient sensing in wireless sensor networks using compressed sensing. Sensors 14(2), 2822–2859 (2014)
Do, T.T.; Tran, T.D.; Gan, L. : Fast compressive sampling with structurally random matrices. In: IEEE International Conference on Acoustics, Speech and Signal Processing 2008. ICASSP 2008, pp. 3369–3372 (2008)
Ravelomanantsoa, A.; Rabah, H.; Rouane, A.: Simple and efficient compressed sensing encoder for wireless body area network. IEEE Trans. Instrum. Meas. 63(11), 2973–2982 (2014)
Mallat, S.G.; Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41(11), 3397–3415 (1993)
Shen, Y.; Li, B.; Pan, W.; Li, J.: Analysis of generalised orthogonal matching pursuit using restricted isometry constant. Electron. Lett. 50(14), 1020–1022 (2014)
Li, B.; Shen, Y.; Wu, Z.; Li, J.: Sufficient conditions for generalized orthogonal matching pursuit in noisy case. Sig. Process. 108, 111–123 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Goyal, P., Singh, B. Greedy algorithms for sparse signal recovery based on temporally correlated experimental data in WSNs. Arab J Sci Eng 43, 7253–7264 (2018). https://doi.org/10.1007/s13369-017-3001-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-017-3001-5