Wireless Personal Communications

, Volume 97, Issue 3, pp 4773–4787 | Cite as

Image Compression Using Two Dimensional DCT and Least Squares Interpolation

  • Sameh A. EisaEmail author
  • Waleed Lotfy


This paper introduces a new image compression method utilizing a combination of discrete cosine transform and least squares interpolation method. Presented is a discussion of the mathematical background, outline of the approach, complexity computations, pseudocode, and an explanation of how to implement the algorithm for applications that require the coded bits to be binary streams. We then provide the results, including comparisons to many recently published works. The results indicate positive progress and effectiveness of the new approach in terms of comparability to other works and applicability in real time applications.


Image compression Signal processing LSM interpolation DCT 



The authors of this research would like to show their gratitude to Skye Eisa, Dual M.A., LPCC for help in presenting the research findings through suggestions and editing of this text.


  1. 1.
    Joseph, B. A., Ramachandran, B. (2012). Enhanced quality preserved image compression technique using edge assisted wavelet based interpolation. In P. S. Thilagam et al. (Eds.), ADCONS 2011: Advanced Computing, Networking and Security (vol. 7135, pp. 146–153). Berlin: Springer-Verlag.Google Scholar
  2. 2.
    Ouafi, A., Ahmed, A. T., Baarir, Z., & Zitouni, A. (2008). A modified embedded zerotree wavelet (MEZW) algorithm for image compression. Journal of Mathematical Imaging and Vision, 30, 298–307.CrossRefGoogle Scholar
  3. 3.
    Averbuch, A. Z., & Zheludev, V. A. (2004). A new family of spline-based biorthogonal wavelet transforms and their application to image compression. IEEE Transaction on Image Processing, 13(7), 993–1007.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Giurcaneanu, C. D., & Tabus, I. (2002). Optimal coding of quantized Laplacian sources for predictive image compression. Journal of Mathematical Imaging and Vision, 16, 251–268.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Franssens, G., De Maziere, M., Fonteyn, D., & Fussen, D. (1998) Image compression based on a multipoint Taylor series representation. In International symposium on computer graphics, image processing, and vision (SIBGRAPI ‘98). Google Scholar
  6. 6.
    Bailo, G., Bariani, M., Chiappori, A., & Stagnaro, R. (2006). Adaptive interpolation algorithm for fast and efficient video encoding in H.26. In 14th European signal processing conference (EUSIPCO 2006), Florence. Google Scholar
  7. 7.
    Lütai, G., & Feng, L. (2001). A method with scattered data spline and wavelets for image compression. In Y. Y. Tang, et al. (Eds.), Wavelet Analysis and Its Applications (vol. 2251, pp. 49–53). Berlin: Springer-Verlag.Google Scholar
  8. 8.
    Ajorloo, H., Manzuri-Shalmani, M. T., & Lakdashti, A. (2007). A Lagrange interpolation based error correction coding for the images. In Proceedings of the 5th international symposium on image and signal processing and analysis. Google Scholar
  9. 9.
    Oh, H., Lee, J., Min, C., & Jeong, J. (2010). Frame interpolation method based on adaptive threshold and adjacent pixels. In 2010 Sixth international conference on intelligent information hiding and multimedia signal processing. Google Scholar
  10. 10.
    Rajakumar, K., & Arivoli, T. (2015). Lossy image compression using multiwavelet transform for wireless transmission. Wireless Personal Communications, 87, 315–333.CrossRefGoogle Scholar
  11. 11.
    Das, M., Nethercott, J., & Rahrig, F. W. (1996). An efficient lossless image compression scheme for hierarchical, block-by-block transmission. In IEEE 39th Midwest symposium on circuits and systems (vol. 2).Google Scholar
  12. 12.
    Fahmy, M. F., Fahmy, G., & Fahmy, O. F. (2011). B-spline wavelets for signal denoising and image compression. Signal, Image and Video Processing, 5, 141–153.CrossRefGoogle Scholar
  13. 13.
    Fahmy, M. F., & Fahmy, G. (2012). C12. Image compression using exponential b-spline functions. In 29th national radio science conference (NRSC 2012). Google Scholar
  14. 14.
    Franti, P., Ageenko, E. I., & Kolesnikov, A. (1999). Vectorising and feature-based filtering for line-drawing image compression. Pattern Analysis and Applications, 2, 285–291.CrossRefGoogle Scholar
  15. 15.
    Prabhakaran, P. J., & Poonacha, P. G. (2015). A new decimation and interpolation algorithm and an efficient lossless compression technique for images. In 2015 twenty first national conference on communications (NCC). Google Scholar
  16. 16.
    Eisa, S. A. N. (2014). Numerical curve length calculation using polynomial interpolation. Journal of Mathematical Imaging and Vision, 49, 377–383.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Eisa, S. A. N. (2014). Three audio CODECs using the LSM interpolation and comparison with PCM. British Journal of Mathematics & Computer Science, 4(10), 1365–1380.CrossRefGoogle Scholar
  18. 18.
    Yin, S., & Balchen, J. G. (1997). Image compression and transmission through a low-rate ultrasonic link in subsea telerobotic applications. Journal of Mathematical Imaging and Vision, 7, 41–53.CrossRefGoogle Scholar
  19. 19.
    Lin, T. C., Truong, T. K., Chen, S. H., Lin, C. C., & Chen, P. D. (2006). DCT-based image CODEC embedded cubic spline interpolation with optimal quantization. In Proceedings of the eighth IEEE international symposium on multimedia (ISM’06). Google Scholar
  20. 20.
    Bastani, V., Helfroush, M. S., & Kasiri, K. (2010). Image compression based on spatial redundancy removal and image inpainting. Journal of Zhejiang University Science C (Comput & Electron), 11(2), 92–100.CrossRefGoogle Scholar
  21. 21.
    Chen, X., & Cheng, A. M. K. (1997). An imprecise algorithm for real-time compressed image and video transmission. In Sixth international conference on computer communications and networks. Google Scholar
  22. 22.
    Algorithm and formula of two dimensional DCT in Mathworks for Matlab implementation:
  23. 23.
    Algorithm and formula of two dimensional Inverse DCT in Mathworks for Matlab implementation:

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsNew Mexico TechSocorroUSA
  2. 2.AlexandriaEgypt

Personalised recommendations