Skip to main content
Log in

A new structure of spline wavelet transform based on adaptive directional lifting for efficient image coding

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

We present in this paper a modified structure of a polynomial spline wavelet transform based on adaptive directional lifting for image compression. The proposed method not only uses the polynomial splines as a tool for the construction of the appropriate filters seeing its efficiency as compared to other filters like the biorthogonal 9/7, but also adapts far better to the image-orientation features by carrying out a lifting-based prediction in local windows in the direction of high pixel correlation. The main purpose of this article is then to integrate the coefficients calculated by the best spline filter order into the adaptive directional lifting. The new method is designed to further reduce the magnitude of the high-frequency wavelet coefficients and preserve the detailed information of the original images more effectively. The numerical results demonstrate the efficiency of the proposed approach over the traditional lifting-based spline wavelet transform and the adaptive directional lifting with respect to both objective and subjective criteria for image compression applications.

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

Access this article

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

Similar content being viewed by others

References

  1. Taubman, D.: Adaptive, non-separable lifting transforms for image compression. In: International Conference on Image Processing, 1999. ICIP 99. Proceedings. 1999, vol. 3, pp. 772–776. IEEE (1999)

  2. Claypoole, R., Davis, G., Sweldens, W., Baraniuk, R.: Nonlinear wavelet transforms for image coding via lifting. IEEE Trans. Image Process. 12(12), 1449–1459 (2003)

    Article  MathSciNet  Google Scholar 

  3. Gerek, O.N., Çetin, A.E.: A 2-d orientation-adaptive prediction filter in lifting structures for image coding. IEEE Trans. Image Process. 15(1), 106–111 (2006)

    Article  Google Scholar 

  4. Chuo-Ling, C., Maleki, A., Girod, B.: Adaptive wavelet transform for image compression via directional quincunx lifting. In: IEEE 7th Workshop on, Multimedia Signal Processing, pp. 1–4 (2005)

  5. Chang, C.-L., Girod, B.: Direction-adaptive discrete wavelet transform via directional lifting and bandeletization. In: IEEE International Conference on Image Processing, 2006, pp. 1149–1152. IEEE (2006)

  6. Chang, C.-L., Girod, B.: Direction-adaptive discrete wavelet transform for image compression. IEEE Trans. Image Process. 16(5), 1289–1302 (2007)

    Article  MathSciNet  Google Scholar 

  7. Ding, W., Feng, W., Li, S.: Lifting-based wavelet transform with directionally spatial prediction. Pict. Coding Symp. 62, 291–294 (2004)

    Google Scholar 

  8. Ding, W., Feng, W., Xiaolin, W., Li, S., Li, H.: Adaptive directional lifting-based wavelet transform for image coding. IEEE Trans. Image Process. 16(2), 416–427 (2007)

    Article  MathSciNet  Google Scholar 

  9. Chen, J., Zengwei, J., Hua, C., Ma, B., Chen, C., Qin, L., Li, R.: Accelerated implementation of adaptive directional lifting-based discrete wavelet transform on gpu. Signal Process. Image Commun. 28(9), 1202–1211 (2013)

    Article  Google Scholar 

  10. Hsia, C.-H., Guo, J.-M.: Efficient modified directional lifting-based discrete wavelet transform for moving object detection. Signal Process. 96, 138–152 (2014)

    Article  Google Scholar 

  11. Sharmila, T.S., Ramar, K.: Efficient analysis of hybrid directional lifting technique for satellite image denoising. Signal Image Video Process. 8(7), 1399–1404 (2014)

    Article  Google Scholar 

  12. Bamberger, R.H., Smith, M.: A filter bank for the directional decomposition of images: theory and design. IEEE Trans. Signal Process. 40(4), 882–893 (1992)

    Article  Google Scholar 

  13. Starck, J.-L., Candès, E.J., Donoho, D.L.: The curvelet transform for image denoising. IEEE Trans. Image Process. 11(6), 670–684 (2002)

    Article  MathSciNet  Google Scholar 

  14. Do, M.N., Vetterli, M.: The finite ridgelet transform for image representation. IEEE Trans. Image Process. 12(1), 16–28 (2003)

    Article  MathSciNet  Google Scholar 

  15. Lisowska, A.: Second order wedgelets in image coding. In: EUROCON, 2007. The International Conference on “Computer as a Tool”, pp. 237–244. IEEE (2007)

  16. Velisavljevic, V., Dragotti, P.L., Vetterli, M.: Directional wavelet transforms and frames. In: 2002 International Conference on Image Processing. 2002. Proceedings, vol. 3, pp. 589–592. IEEE (2002)

  17. Peyré, G., Mallat, S.: Surface compression with geometric bandelets. ACM Trans. Graph. 24(3), 601–608 (2005)

    Article  Google Scholar 

  18. Kamble, V.M., Parlewar, P., Keskar, A.G., Bhurchandi, K.M.: Performance evaluation of wavelet, ridgelet, curvelet and contourlet transforms based techniques for digital image denoising. Artif. Intell. Rev. 45, 509–533 (2016)

    Article  Google Scholar 

  19. Hacene, I.B., Bessaid, A.: Greyscale and colour medical image compressed using hybrid contourlet biorthogonal cdf lifting scheme, bandelet and quincunx wavelet transforms: a comparative study. Int. J. Biomed. Eng. Technology 26, 13–31 (2018)

    Google Scholar 

  20. Limaye, M., Paithane, A.: Implementing image compression using transform based approach. In: International Conference on Computing Methodologies and Communication, pp. 834–840. IEEE (2017)

  21. Mallat, S.: Geometrical grouplets. Appl. Comput. Harmon. Anal. 26, 161–180 (2009)

    Article  MathSciNet  Google Scholar 

  22. Krommweh, J.: Tetrolet transform: a new adaptive haar wavelet algorithm for sparse image representation. J. Vis. Commun. Image Represent. 21, 364–374 (2010)

    Article  Google Scholar 

  23. Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 6, 679–698 (1986)

    Article  Google Scholar 

  24. Hamdi, M., Rhouma, R., Belghith, S.: A selective compression-encryption of images based on spiht coding and chirikov standard map. Signal Process. 131, 514–526 (2017)

    Article  Google Scholar 

  25. Zhang, L., Qiu, B.: Edge-preserving image compression using adaptive lifting wavelet transform. Int. J. Electron. 102(7), 1190–1203 (2015)

    Article  Google Scholar 

  26. Boujelbene, R., Jemaa, Y.B., Zribi, M.: Toward an optimal b-spline wavelet transform for image compression. In: IEEE/ACS 13th International Conference of Computer Systems and Applications (AICCSA), 2016, pp. 1–8. IEEE (2016)

  27. Boujelbene, R., Jemaa, Y.B., Zribi, M.: An efficient codec for image compression based on spline wavelet transform and improved spiht algorithm. In: International Conference on High Performance Computing & Simulation (HPCS), 2017, pp. 819–825. IEEE (2017)

  28. Sweldens, W.: The lifting scheme: a custom-design construction of biorthogonal wavelets “industrial mathematics initiative” technical report 1994: 7, Department of Mathematical, University of South Carolina, Columbia (1994)

  29. Yaroslavsky, L.: Fast signal sinc-interpolation methods for signal and image resampling. In: Image Processing: Algorithms and Systems, vol. 4667, pp. 120–130. International Society for Optics and Photonics (2002)

  30. Breiman, L. Classification and regression trees, ser. wadsworth statistics/probability series. Wadsworth International Group (1984)

  31. Boujelbene, R., Jemaa, Y.B., Zribi, M.: A comparative study of recent improvements in wavelet-based image coding schemes. Multimed. Tools Appl. 78(2), 1649–1683 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Dr. J. Chen, Huazhong University of Science and Technology, for many insightful discussions on the topic.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rania Boujelbene.

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

Boujelbene, R., Ben Jemaa, Y. A new structure of spline wavelet transform based on adaptive directional lifting for efficient image coding. SIViP 14, 1451–1459 (2020). https://doi.org/10.1007/s11760-020-01685-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-020-01685-5

Keywords

Navigation