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On the design of KLT-based maximally incoherent deterministic sensing matrices for compressive sensing applied to wireless sensor networks data

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Abstract

The Compressive Sensing (CS) framework explores signal sparsity to reduce the amount of data to transmit or store. In it, signal projections on sensing vectors are used to measure the signal, the set of sensing vectors compose the sensing matrix. Usually, one constructs the sensing matrix to be incoherent to a basis in which the signal is sparse. In this paper, we propose and investigate the use of Karhunen–Loève Transforms (KLTs) as sparsifying bases to construct the corresponding maximally incoherent deterministic sensing matrices. This is done within the context of encoding environmental signals acquired by a Wireless Sensor Network (WSN). The Rate\(\times\)Distortion (RD) performance of the CS encoding-decoding scheme when the KLT-based deterministic sensing matrices are used is compared against the ones obtained when the CS scheme builds on either the Discrete Cosine Transform (DCT-based) or the K Singular Value Decomposition (K-SVD-based) as sparsifying basis to construct the deterministic sensing matrix. To this end, we also investigate the impact, on the K-SVD-based CS, of the number of elements used to express signals using the K-SVD algorithm. The experimental results show that the proposed KLT-based sensing matrices outperform the DCT- and the K-SVD based alternatives in terms of recovered signal quality, encoding bitrate, and computational cost, which, in WSN applications, is a proxy to energy consumption.

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Notes

  1. For the K-SVD, since K is the a priori sparsity and the signal block length is \(N=512\), the maximum number of measurements M is equal to \(\frac{N}{2}\)=256, \(\frac{N}{4}\)=128, \(\frac{N}{8}\)=64 and \(\frac{N}{16}\)=32, respectively.

  2. The same behavior was also observed when the KLT-based maximally incoherent sensing matrix was compared to the K-SVD-based sensing matrices with \(K = N\) and \(K = \frac{N}{2}\).

References

  1. Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.

    Article  MathSciNet  MATH  Google Scholar 

  2. Candès, E., Romberg, J., & Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52(2), 489–509.

    Article  MathSciNet  MATH  Google Scholar 

  3. Laska, J. N., Boufounos, P. T., & Davenport, M. A. (2011). Democracy in action: Quantization, saturation and compressive sensing. Applied and Computational Harmonic Analysis, 31(3), 429–443.

    Article  MathSciNet  MATH  Google Scholar 

  4. Candes, E. J., & Wakin, M. B. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21–30.

    Article  Google Scholar 

  5. Coifman, R., Geshwind, F., & Meyer, Y. (2001). Noiselets. Applied and Computational Harmonic Analysis, 10(1), 27–44.

    Article  MathSciNet  MATH  Google Scholar 

  6. Nguyen, T. L., & Shin, Y. (2013). Deterministic sensing matrices in compressive sensing: A survey. The Scientific World Journal

  7. Lovisolo, L., Pereira, M. P., da Silva, E. A. B., & Campos, M. L. R. (2014). On the design of maximally incoherent sensing matrices for compressed sensing and its extension for biorthogonal bases case. Digital Signal Processing, 27, 12–22.

    Article  Google Scholar 

  8. Dehghannasiri, R., Qian, X., & Dougherthy, E. W. (2018). Intrinsically Bayesian Robust Karhunen-Loève compression. Signal Processing, 144, 311–322.

    Article  Google Scholar 

  9. Jain, A. K. (1989). Fundamentals of digital image processing. Englewood Cliffs, NJ: Prentice Hall.

    MATH  Google Scholar 

  10. Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., & Cayirci, E. (2002). Wireless sensor networks: A survey. Computer Networks, 38(4), 393–422.

    Article  Google Scholar 

  11. Henriques, F. R., Lovisolo, L., & Rubinstein, M. G. (2016). DECA: Distributed energy conservation algorithm for process reconstruction with bounded relative error in wireless sensor networks. EURASIP Journal on Wireless Communications and Networking, 2016(163), 1–18.

    Google Scholar 

  12. Yang, L., Zhu, H., Wang, H., Kang, K., & Qian, H. (2019). Data censoring with network lifetime constraint in wireless sensor networks. Digital Signal Processing, 92, 73–81.

    Article  Google Scholar 

  13. Yetgin, H., Cheung, K. T. K., El-Hajjar, M., & Hanzo, L. H. (2017). A survey of network lifetime maximization techniques in wireless sensor networks. IEEE Communications Surveys Tutorials, 19(2), 828–854.

    Article  Google Scholar 

  14. Li, X., Tao, X., & Chen, Z. (2018). Spatio-temporal compressive sensing-based data gathering in wireless sensor networks. IEEE Wireless Communications Letters, 7(2), 198–201.

    Article  Google Scholar 

  15. Wang, W., Wang, D., & Jiang, Y. (2017). Energy efficient distributed compressed data gathering for sensor networks. Ad Hoc Networks, 58, 112–117.

    Article  Google Scholar 

  16. Henriques, F. R., Lovisolo, L., & da Silva, E. A. B. (2019). Rate-distortion performance and incremental transmission scheme of compressive sensed measurements in wireless sensor networks. Sensors, 19(2)

  17. Aharon, M., Elad, M., & Bruckstein, A. (2006). K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 54(11), 4311–4322.

    Article  MATH  Google Scholar 

  18. Fei, Z., Lin, F., Chen, J., & Wan, J. (2017). Unit orthogonal Atom K-SVD algorithm for compressed signals in wireless sensor networks. In: 2017 9th International conference on intelligent human-machine systems and cybernetics (IHMSC), Vol. 2, pp. 25–28.

  19. Jiang, Q., & Matic, R. (2009). Modulation classification based compressed sensing for communication signals. In: Sensors, and command, control, communications, and intelligence (C3I) technologies for homeland security and homeland defense VIII, vol. 7305, pp. 335–346.

  20. Kuo, P., Kung, H. T., & Ting, P. (2012). Compressive sensing based channel feedback protocols for spatially-correlated massive antenna arrays. In: 2012 IEEE wireless communications and networking conference (WCNC), pp. 492–497.

  21. Dumitrescu, B., & Irofti, P. (2018). Dictionary learning algorithms and applications. Switzerland: Springer.

    Book  MATH  Google Scholar 

  22. De, P., Chatterjee, A., & Rakshit, A. (2021). Regularized K-SVD-based dictionary learning approaches for PIR sensor-based detection of human movement direction. IEEE Sensors Journal, 21(5), 6459–6467.

    Article  Google Scholar 

  23. He, H., Li, H., Huang, Y., Huang, J., & Li, P. (2020). A novel efficient camera calibration approach based on K-SVD sparse dictionary learning. Measurement, 159, 1–12.

    Article  Google Scholar 

  24. Cleju, N., & Ciocoiu, I. B. (2020). Preconditioned K-SVD for ECG anomaly detection. In: 2020 international symposium on electronics and telecommunications (ISETC), pp. 1–4.

  25. Payani, A., Abdi, A., Tian, X., Fekri, F., & Mohandes, M. (2018). Advances in seismic data compression via learning from data: Compression for seismic data acquisition. IEEE Signal Processing Magazine, 35(2), 51–61.

    Article  Google Scholar 

  26. Mairal, J., Bach, F., Ponce, J., & Sapiro, G. (2009). Online dictionary learning for sparse coding. In: Proceedings of the 26th annual international conference on machine learning. ICML ’09, pp. 689–696. Association for Computing Machinery, New York

  27. Shen, Z. Y., Cheng, X. M., & Wang, Q. Q. (2020). A cooperative construction method for the measurement matrix and sensing dictionary used in compression sensing. EURASIP Journal on Advances in Signal Processing, 2020(10), 1–8.

    Google Scholar 

  28. Sarwate, D. V. (1999). Sequences and their applications. Korea: Springer.

    Google Scholar 

  29. Nouasria, H., & Et-tolba, M. (2018). Sensing matrix based on Kasami codes for compressive sensing. IET Signal Processing, 12(8), 1064–1072.

    Article  Google Scholar 

  30. Nouasria, H., & Et-tolba, M. (2019). A novel deterministic sensing matrix based on Kasami codes for cluster structured sparse signals. In: ICASSP 2019–2019 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp. 1592–1596.

  31. Yu, L., Sun, H., Barbot, J. P., & Zheng, G. (2012). Bayesian compressive sensing for cluster structured sparse signals. Signal Processing, 92(1), 259–269.

    Article  Google Scholar 

  32. Candès, E., & Romberg, J. (2005). L1–magic.

  33. Karahanoglu, N. B., & Erdogan, H. (2012). A* orthogonal matching pursuit: Best-first search for compressed sensing signal recovery. Digital Signal Processing, 22(4), 1–20.

    Article  MathSciNet  Google Scholar 

  34. Tibshirani, R. (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society, 58(1), 267–288.

    MathSciNet  MATH  Google Scholar 

  35. van den Berg, E., & Friedlander, M. P. (2007). SPGL1: A solver for large-scale sparse reconstruction. http://www.cs.ubc.ca/labs/scl/spgl1

  36. Chen, W., Rodrigues, M. R. D., & Wassel, I. J. (2011). Distributed compressive sensing reconstruction via common support discovery. In: proceedings of the IEEE international conference on communications, pp. 1–5.

  37. lab WSN, I. B. (2004). http://db.csail.mit.edu/labdata/labdata.html (2004)

  38. Rubinstein, R., Zibulevsky, M., & Elad, M. (2008). Efficient implementation of the k-svd algorithm using batch orthogonal matching pursuit. Computer Science Department, Technion: Technical report.

  39. Feng, H., & Effros, M. (2002). On the rate-distortion performance and computational efficiency of the Karhunen–Loeve transform for lossy data compression. IEEE Transactions on Image Processing, 11(2), 113–122.

    Article  MathSciNet  Google Scholar 

  40. Cervin, A., Herinksson, D., Lincoln, B., Eker, J., & Arzèn, K.-E. (2003). How does control timing affect performance? Analysis and simulation of timing using jitterbug and truetime. IEEE Control Systems Magazine, 23(3), 16–30.

    Article  Google Scholar 

  41. Baronti, P., Pillai, P., Chook, V., Chessa, S., Gotta, A., & Hu, Y. F. (2007). Wireless sensor networks: A survey on the state of art and the 802154 and ZigBee Standards. Computer Communications, 30(7), 1655–1695.

    Article  Google Scholar 

  42. Varga, A. (2010). Omnet++. In: Modeling and tools for network simulation, pp. 35–59

  43. Boulis, A. (2011). Castalia user’s manual. Marzo del: NICTA.

    Google Scholar 

  44. de Ferreira, C. B. M., Guedes, R. M., & Henriques, F. D. R.: Cluster-head switching algorithm based on node temperature in wireless body sensors networks. In: Proceedings of the 25th Brazillian symposium on multimedia and the web, pp. 65–72 (2019)

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Acknowledgements

This work was partially supported by Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ)—Reference: 210.286/2019.

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Authors and Affiliations

  1. PPCIC, PPGIO, Coordenação de Telecomunicações - CEFET/RJ, Petrópolis, Rio de Janeiro, Brazil

    Felipe da Rocha Henriques

  2. DETEL/PEL/UERJ, Rio de Janeiro, RJ, Brazil

    Lisandro Lovisolo

  3. PEE/COPPE/UFRJ, Rio de Janeiro, RJ, Brazil

    Eduardo Antônio Barros da Silva

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  1. Felipe da Rocha Henriques
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  2. Lisandro Lovisolo
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  3. Eduardo Antônio Barros da Silva
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Correspondence to Felipe da Rocha Henriques.

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Henriques, F.d.R., Lovisolo, L. & da Silva, E.A.B. On the design of KLT-based maximally incoherent deterministic sensing matrices for compressive sensing applied to wireless sensor networks data. Wireless Netw 29, 3271–3284 (2023). https://doi.org/10.1007/s11276-023-03383-9

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