Skip to main content
SpringerLink
Log in

Efficient Methods for Signal Processing Using Charlier Moments and Artificial Bee Colony Algorithm

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, we propose efficient methods for the reconstruction, compression, compressive sensing (CS) and encryption of 1D signals. The proposed reconstruction method is based on the use of Charlier moments (CMs) and the Artificial Bee Colony (ABC) algorithm. The latter is used for optimizing the local parameter of Charlier polynomials during the computation of CMs. In addition, new methods are presented for 1D signal compression and CS using CMs and ABC algorithm that guarantees a high quality of the decompressed/reconstructed signal. Moreover, we suggest a new signal encryption/decryption scheme relying on fractional-order Charlier moments and ABC algorithm, which is used for providing a high quality of the decrypted signal and for improving the security of the proposed scheme. The results of the conducted simulations and comparisons clearly show the efficiency of the proposed 1D-signal analysis methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Availability of data and materials

The data used to support the findings of this study are available in [21, 42].

References

  1. J. Afshar Jahanshahi et al., Compressive sensing based the multi-channel ECG reconstruction in wireless body sensor networks. Biomed. Signal Process. Control. 61, 102047 (2020). https://doi.org/10.1016/j.bspc.2020.102047

    Article  Google Scholar 

  2. S. Aslan, D. Karaboga, A genetic Artificial Bee Colony algorithm for signal reconstruction based big data optimization. Appl. Soft Comput. 88, 106053 (2020)

    Article  Google Scholar 

  3. R.V. Babu et al., A survey on compressed domain video analysis techniques. Multimed. Tools Appl. 75(2), 1043–1078 (2016). https://doi.org/10.1007/s11042-014-2345-z

    Article  Google Scholar 

  4. R.G. Baraniuk, Compressive sensing [lecture notes]. IEEE Signal Process. Mag. 24(4), 118–121 (2007)

    Article  Google Scholar 

  5. A. Bendifallah et al., Improved ECG compression method using discrete cosine transform. Electron. Lett. 47(2), 87–89 (2011)

    Article  Google Scholar 

  6. R. Benouini et al., Fast and accurate computation of Racah moment invariants for image classification. Pattern Recognit. 91, 100–110 (2019). https://doi.org/10.1016/j.patcog.2019.02.014

    Article  Google Scholar 

  7. T.W. Cabral, et al., Compressive sensing in medical signal processing and imaging systems, in Sensors for Health Monitoring, pp. 69–92. Elsevier (2019).

  8. C. Camacho-Bello, J.S. Rivera-Lopez, Some computational aspects of Tchebichef moments for higher orders. Pattern Recognit. Lett. 112, 332–339 (2018). https://doi.org/10.1016/j.patrec.2018.08.020

    Article  Google Scholar 

  9. E.J. Candès et al., Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory. 52(2), 489–509 (2006)

    Article  MathSciNet  Google Scholar 

  10. A. Daoui et al., Biomedical signals reconstruction and zero-watermarking using separable fractional order Charlier-Krawtchouk transformation and sine cosine algorithm (SCA). Signal Process. (2020). https://doi.org/10.1016/j.sigpro.2020.107854

    Article  Google Scholar 

  11. A. Daoui et al., Efficient computation of high-order Meixner moments for large-size signals and images analysis. Multimed. Tools Appl. (2020). https://doi.org/10.1007/s11042-020-09739-z

    Article  Google Scholar 

  12. A. Daoui, et al., Efficient reconstruction and compression of large size ECG signal by Tchebichef moments, in 2020 International Conference on Intelligent Systems and Computer Vision (ISCV), pp. 1–6 (2020). https://doi.org/10.1109/ISCV49265.2020.9204132

  13. A. Daoui et al., Fast and stable bio-signals reconstruction using Krawtchouk moments. Adv. Intell. Syst. Comput. 1076, 369–377 (2020). https://doi.org/10.1007/978-981-15-0947-6_35

    Article  Google Scholar 

  14. A. Daoui et al., New algorithm for large-sized 2D and 3D image reconstruction using higher-order Hahn moments. Circuits Syst. Signal Process. (2020). https://doi.org/10.1007/s00034-020-01384-z

    Article  Google Scholar 

  15. A. Daoui et al., New robust method for image copyright protection using histogram features and Sine Cosine Algorithm. Expert Syst. Appl. 177, 114978 (2021)

    Article  Google Scholar 

  16. A. Daoui et al., Stable computation of higher order Charlier moments for signal and image reconstruction. Inf. Sci. 521, 251–276 (2020). https://doi.org/10.1016/j.ins.2020.02.019

    Article  MATH  Google Scholar 

  17. D.L. Donoho, Compressed sensing. IEEE Trans. Inf. Theory. 52(4), 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  18. F. Ernawan et al., An efficient image compression technique using Tchebichef bit allocation. Optik 148, 106–119 (2017). https://doi.org/10.1016/j.ijleo.2017.08.007

    Article  Google Scholar 

  19. A. Fathi, F. Faraji-kheirabadi, ECG compression method based on adaptive quantization of main wavelet packet subbands. Signal Image Video Process. 10(8), 1433–1440 (2016). https://doi.org/10.1007/s11760-016-0944-z

    Article  Google Scholar 

  20. J. Flusser et al., 2D and 3D Image Analysis by Moments (Wiley, New York, 2016)

    Book  Google Scholar 

  21. J. Garofolo, L. Lamel, W. Fisher, J. Fiscus, D. Pallett, N. Dahlgren, V. Zue, TIMIT Acoustic-Phonetic Continuous Speech Corpus (Abacus Data Network, 1993). https://hdl.handle.net/11272.1/AB2/SWVENO

  22. A. Hmimid et al., Fast computation of separable two-dimensional discrete invariant moments for image classification. Pattern Recognit. 48(2), 509–521 (2015). https://doi.org/10.1016/j.patcog.2014.08.020

    Article  MATH  Google Scholar 

  23. A. Hmimid et al., Image classification using separable invariant moments of Charlier-Meixner and support vector machine. Multimed. Tools Appl. 77(18), 23607–23631 (2018)

    Article  Google Scholar 

  24. K.M. Hosny et al., Efficient compression of bio-signals by using Tchebichef moments and Artificial Bee Colony. Biocybern. Biomed. Eng. 38(2), 385–398 (2018). https://doi.org/10.1016/j.bbe.2018.02.006

    Article  MathSciNet  Google Scholar 

  25. T. Jahid et al., Image analysis by Meixner moments and a digital filter. Multimed. Tools Appl. 77(15), 19811–19831 (2018)

    Article  Google Scholar 

  26. T. Jahid, et al., Image moments and reconstruction by Krawtchouk via Clenshaw’s reccurence formula, in 2017 International Conference on Electrical and Information Technologies (ICEIT), pp. 1–7 IEEE (2017).

  27. C.K. Jha, M.H. Kolekar, Electrocardiogram data compression using DCT based discrete orthogonal Stockwell transform. Biomed. Signal Process. Control. 46, 174–181 (2018)

    Article  Google Scholar 

  28. E.G. Karakasis et al., Generalized dual Hahn moment invariants. Pattern Recognit. 46(7), 1998–2014 (2013). https://doi.org/10.1016/j.patcog.2013.01.008

    Article  MATH  Google Scholar 

  29. H. Karmouni et al., Fast and stable computation of the charlier moments and their inverses using digital filters and image block representation. Circuits Syst. Signal Process. 37(9), 4015–4033 (2018). https://doi.org/10.1007/s00034-018-0755-2

    Article  MathSciNet  Google Scholar 

  30. H. Karmouni et al., Fast computation of 3D discrete invariant moments based on 3D Cuboid for 3D image classification. Circuits Syst. Signal Process. 5, 1–31 (2021)

    Google Scholar 

  31. H. Karmouni et al., Fast computation of inverse Meixner moments transform using Clenshaw’s formula. Multimed. Tools Appl. 78(22), 31245–31265 (2019). https://doi.org/10.1007/s11042-019-07961-y

    Article  Google Scholar 

  32. H. Karmouni et al., Fast reconstruction of 3D images using Charlier discrete orthogonal moments. Circuits Syst. Signal Process. 38(8), 3715–3742 (2019)

    Article  MathSciNet  Google Scholar 

  33. H. Karmouni, et al., Image analysis using separable Krawtchouk-Tchebichef’s moments, in 2017 International Conference on Advanced Technologies for Signal and Image Processing (ATSIP), pp. 1–5 IEEE (2017).

  34. H. Karmouni, et al., Image reconstruction by Krawtchouk moments via digital filter, in 2017 Intelligent Systems and Computer Vision (ISCV), pp. 1–7 IEEE (2017)

  35. O. Kerdjidj et al., An FPGA implementation of the matching pursuit algorithm for a compressed sensing enabled e-Health monitoring platform. Microprocess. Microsyst. 67, 131–139 (2019)

    Article  Google Scholar 

  36. R. Koekoek et al., Hypergeometric Orthogonal Polynomials and Their Q-Analogues (Springer, Berlin, 2010)

    Book  Google Scholar 

  37. A. Kulkarni, T. Mohsenin, Low overhead architectures for OMP compressive sensing reconstruction algorithm. IEEE Trans. Circuits Syst. Regul. Pap. 64(6), 1468–1480 (2017)

    Article  Google Scholar 

  38. S. Kumar et al., Multichannel ECG compression using Block-Sparsity-based joint compressive sensing. Circuits Syst. Signal Process. 39(12), 6299–6315 (2020). https://doi.org/10.1007/s00034-020-01483-x

    Article  Google Scholar 

  39. W.S. Lang, et al., Fast 4x4 Tchebichef moment image compression, in 2009 International Conference of Soft Computing and Pattern Recognition, pp. 295–300. IEEE (2009)

  40. X. Liu et al., Fractional Krawtchouk transform with an application to image watermarking. IEEE Trans. Signal Process. 65(7), 1894–1908 (2017). https://doi.org/10.1109/TSP.2017.2652383

    Article  MathSciNet  MATH  Google Scholar 

  41. H. Mohimani et al., A fast approach for overcomplete sparse decomposition based on smoothed $$\backslash$ell^${$0$}$ $ norm. IEEE Trans. Signal Process. 57(1), 289–301 (2008)

    Article  MathSciNet  Google Scholar 

  42. G.B. Moody, R.G. Mark, MIT-BIH Arrhythmia Database. httpssss://physionet.org/content/mitdb/. doi:10.13026/C2F305 (1992)

  43. G.B. Moody, R.G. Mark, The impact of the MIT-BIH arrhythmia database. IEEE Eng. Med. Biol. Mag. 20(3), 45–50 (2001)

    Article  Google Scholar 

  44. R. Mukundan et al., Image analysis by Tchebichef moments. IEEE Trans. Image Process. 10(9), 1357–1364 (2001)

    Article  MathSciNet  Google Scholar 

  45. R. Mukundan, Some computational aspects of discrete orthonormal moments. IEEE Trans. Image Process. 13(8), 1055–1059 (2004)

    Article  MathSciNet  Google Scholar 

  46. O.E. Ogri et al., 2D and 3D medical image analysis by discrete orthogonal moments. Procedia Comput. Sci. 148, 428–437 (2019). https://doi.org/10.1016/j.procs.2019.01.055

    Article  Google Scholar 

  47. S.M.M. Rahman et al., On the selection of 2D Krawtchouk moments for face recognition. Pattern Recognit. 54, 83–93 (2016). https://doi.org/10.1016/j.patcog.2016.01.003

    Article  Google Scholar 

  48. B.A. Rajoub, An efficient coding algorithm for the compression of ECG signals using the wavelet transform. IEEE Trans. Biomed. Eng. 49(4), 355–362 (2002)

    Article  Google Scholar 

  49. M. Sayyouri, et al., A fast computation of Hahn moments for binary and gray-scale images, in 2012 IEEE International Conference on Complex Systems (ICCS), pp. 1–6 (2012). https://doi.org/10.1109/ICoCS.2012.6458538.

  50. M. Sayyouri et al., A fast computation of novel set of Meixner invariant moments for image analysis. Circuits Syst. Signal Process. 34(3), 875–900 (2015). https://doi.org/10.1007/s00034-014-9881-7

    Article  Google Scholar 

  51. M. Sayyouri et al., Image analysis using separable discrete moments of Charlier-Tchebichef. Int. J. Circuits Syst. Signal Process. 8, 91–100 (2014)

    Google Scholar 

  52. M. Sayyouri et al., Improving the performance of image classification by Hahn moment invariants. JOSA A. 30(11), 2381–2394 (2013). https://doi.org/10.1364/JOSAA.30.002381

    Article  Google Scholar 

  53. Y. Tsaig, D.L. Donoho, Extensions of compressed sensing. Signal Process. 86(3), 549–571 (2006)

    Article  Google Scholar 

  54. F. Wang et al., A novel ECG signal compression method using spindle convolutional auto-encoder. Comput. Methods Programs Biomed. 175, 139–150 (2019). https://doi.org/10.1016/j.cmpb.2019.03.019

    Article  Google Scholar 

  55. D.S. Watkins, The matrix eigenvalue problem. Soc. Ind. Appl. Math. (2007). https://doi.org/10.1137/1.9780898717808

    Article  MATH  Google Scholar 

  56. B. Xiao et al., Fractional discrete Tchebyshev moments and their applications in image encryption and watermarking. Inf. Sci. 516, 545–559 (2020). https://doi.org/10.1016/j.ins.2019.12.044

    Article  MathSciNet  MATH  Google Scholar 

  57. M. Yamni et al., Fractional Charlier moments for image reconstruction and image watermarking. Signal Process. 171, 107509 (2020). https://doi.org/10.1016/j.sigpro.2020.107509

    Article  Google Scholar 

  58. M. Yamni et al., Influence of Krawtchouk and Charlier moment’s parameters on image reconstruction and classification. Procedia Comput. Sci. 148, 418–427 (2019)

    Article  Google Scholar 

  59. P.-T. Yap et al., Image analysis by Krawtchouk moments. IEEE Trans. Image Process. 12(11), 1367–1377 (2003). https://doi.org/10.1109/TIP.2003.818019

    Article  MathSciNet  Google Scholar 

  60. O. Yildirim et al., An efficient compression of ECG signals using deep convolutional autoencoders. Cogn. Syst. Res. 52, 198–211 (2018). https://doi.org/10.1016/j.cogsys.2018.07.004

    Article  Google Scholar 

  61. H. Zanddizari et al., Increasing the quality of reconstructed signal in compressive sensing utilizing Kronecker technique. Biomed. Eng. Lett. 8(2), 239–247 (2018). https://doi.org/10.1007/s13534-018-0057-4

    Article  Google Scholar 

  62. G. Zhang et al., A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments. Pattern Recognit. Lett. 31(7), 548–554 (2010)

    Article  Google Scholar 

  63. H. Zhu et al., General form for obtaining discrete orthogonal moments. IET Image Process. 4(5), 335–352 (2010). https://doi.org/10.1049/iet-ipr.2009.0195

    Article  MathSciNet  Google Scholar 

Download references

Funding

The authors received no specific funding for this work.

Author information

Authors and Affiliations

  1. Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Achraf Daoui & Mhamed Sayyouri

  2. Laboratory of Electronic Signals and Systems of Information, Dhar El Mahrez Faculty of Science, Sidi Mohamed Ben Abdellah-Fez University, Fez, Morocco

    Hicham Karmouni & Hassan Qjidaa

Authors
  1. Achraf Daoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hicham Karmouni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mhamed Sayyouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hassan Qjidaa
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Achraf Daoui contributed to conceptualization, formal analysis, writing—original draft, and writing—review & editing. Hicham Karmouni contributed to software and validation. Mhamed Sayyouri contributed to methodology, writing—review & editing, and project administration. Hassan Qjidaa contributed to visualization and supervision.

Corresponding author

Correspondence to Achraf Daoui.

Ethics declarations

Conflict of interest

The authors declare that there is no conflicts of interest or competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Daoui, A., Karmouni, H., Sayyouri, M. et al. Efficient Methods for Signal Processing Using Charlier Moments and Artificial Bee Colony Algorithm. Circuits Syst Signal Process 41, 166–195 (2022). https://doi.org/10.1007/s00034-021-01764-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-021-01764-z

Keywords

Search

Navigation