Image Compression Using Spline Based Wavelet Transforms

  • Amir Z. Averbuch
  • Valery A. Zheludev
Part of the Computational Imaging and Vision book series (CIVI, volume 19)


In paper we describe a successful applications of the wavelet transforms to still image compression. The wavelet transforms were designed by the usage of discrete interpolatory splines. These filters outperform the traditional biorthogonal 9/7 filters which are frequenty used in wavelet based compression. The new filters and the biorthogonal 9/7 are incorporated into SPIHT in order to measure and compare their performance with one well known codec.


Filter Bank Image Compression Image Code Lift Scheme Infinite Impulse Response Filter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. E. H. Adelson, E. Simoncelli, and R. Hingorani, Orthogonal pyramid transforms for image coding, Proc. SPIE, vol. 845, Cambridge, MA, Oct. 1987, pp. 50–58.CrossRefGoogle Scholar
  2. M. Antonini, M. Barlaud, P. Mathieu and I. Daubechies, Image Coding using Wavelet Transform, IEEE Transaction on Image Processing, 1(2) :205–220, 1992.CrossRefGoogle Scholar
  3. A. Averbuch, D. Lazar, M. Israeli, Image compression using wavelet transform and multiresolution decomposition, IEEE Trans. on Image Processing, 5: 4:15, Jan. 1996.Google Scholar
  4. A. Z. Averbuch, F. Meyer, J-O Stromberg, Fast Adaptive Wavelet Packet Image Compression, IEEE Trans. on Image Processing, 9: 792–800, May 2000.CrossRefGoogle Scholar
  5. A. Averbuch, R. Nir, Still Image Compression using Coded Multiresolution Tree, Technical Report, Tel Aviv University, 1995.Google Scholar
  6. A. Averbuch, M. Israeli, F. Meyer, Speed vs. Quality in Low Bit-Rate Still Image Compression, it Signal Processing: Inage Communication, 15:231–254, 1999.CrossRefGoogle Scholar
  7. A. Averbuch, A. Pevnyi, V. Zheludev A lifting scheme of biorthogonal wavelet transform based on discrete interpolatory splines, Proc. SPIE Wavelet Applications in Signal and Image Processing VIII, (A. Aldroubi, A. F. Laine; M. A. Unser; Eds.) 4119:564–575, 2000.CrossRefGoogle Scholar
  8. A. Z. Averbuch, A. B. Pevnyi and V. A. Zheludev Butterworth wavelets derived from discrete interpolatory splines: Recursive implementation, to appear in 2001. Signal Processing., Scholar
  9. A. Averbuch, V. Zheludev Construction of biorthogonal discrete wavelet transforms using interpolatory splines, to appear in Applied and Comp. Harmonic Analysis,∽amirGoogle Scholar
  10. G. Battle, A block spin construction of ondelettes. Part I. Lemarié func tion s, Comm. Math. Phys. 110:601–615, 1987.MathSciNetCrossRefGoogle Scholar
  11. Bing-Bing Chai, Jozsef Vass, and Xinhua Zhuang, Significance-Linked Connected Component Analysis for Wavelet Image Coding, IEEE Transaction on Image Processing 8:774–784, June 1999.CrossRefGoogle Scholar
  12. M. Boliek, M. J. Gormish , E. L. Schwartz and A. Keith, Next Generation Image Compression and Manipulation Using CREW, Proc. IEEE ICIP, 1997, gormish.pdf http:/ /www. CREW /CREW.suinmary.htmlGoogle Scholar
  13. R. Buccigrossi and E. P. Siinoncelli, EPWIC: Embedded Predictive Wavelet Image Coder, GRASP Laboratory, TR number 414, Scholar
  14. Calderbank, R. C., Daubechies, I., Sweldens, W., and Yeo, B. L. Wavelet Transforms that Map Integers to Integers, Applied and Computational Harmonic Analysis (ACHA), vol. 5, no. 3, pp. 332–369, 1998, Scholar
  15. C. Chrysafis and A. Ortega, Efficient context-based entropy coding for lossy wavelet image compression, DCC, Data Compression Conference, Snowbird, UT, March 25 - 27, 1997. (.ps version available from chrysafi/Publications.html)Google Scholar
  16. C. K. Chui and J. Z. Wang, On compactly supported spline wavelets and a duality principle, Trans. Amer. Math. Soc. 330:903–915, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  17. R. L. Claypoole Jr., J. M. Davis, W. Sweldens, R. Baraniuk, Nonlinear wavelet transforms for image coding via lifting, submitted to IEEE Trans. Image Proc.. Google Scholar
  18. Coifman, R. R. and Wickerhauser, M. V., Entropy Based Algorithms for Best Basis Selection, IEEE Trans. Information Theory, 38:713–718, Mar. 1992.zbMATHCrossRefGoogle Scholar
  19. A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Commun. on Pure and A ppl. Math.’ 45:485–560, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  20. I. Daubechies, Ten lectures on wavelets, SIAM. Philadelphia, PA, 1992.zbMATHCrossRefGoogle Scholar
  21. I. Daubechies, W. Sweldens, Factoring wavelet transforms into lifting steps, J. Fourier Anal. A ppl. 4: 247–269, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  22. D. L. Donoho, Interpolating wavelet transform, Preprint 408, Department of Statistics, Stanford University, 1992.Google Scholar
  23. J. Froment and S. Mallat, Second generation compact image coding with wavelets. in: Wavelets: A Tutorial in Theory and Applications, C.K. Chui, editor, vol. 2, Academic Press, NY, 1992.Google Scholar
  24. C. Herley and M. Vetterli, Wavelets and recursive filter banks, IEEE Trans. Signal Proc.,’ 41(12) :2536–2556 1993.zbMATHCrossRefGoogle Scholar
  25. R. Joshi, H. Jafarkhani, J. Kasner, T. Fischer, N. Farvardin, M. Marcellin and R. Bamberger, Comparison of Different Methods of Classification in Subband Coding of Images, IEEE Trans. Image Proc., 6:1473–1487, November 1997.CrossRefGoogle Scholar
  26. P. G. Lernarié, Ondelettes à localisation exponentielle, J. de Math. Pures et A ppl. 67:227–236, 1988.Google Scholar
  27. S. M. LoPresto, K. Ramchandran, and M.T. Orchard, Image coding based on mixture modeling of wavelet coefficients and a fast estimationquantization framework, it IEEE Data Compression Conference ’97 Proceedings, pp. 221–230, March 1997.Google Scholar
  28. D. Marpe and H.L. Cycon, Efficient Pre-Coding Techniques for WaveletBased Iniage Compression, submitted to PCS, Berlin, 1997. For more information. please see Google Scholar
  29. D. Marpe, G. Heising, A. P. Petukhov, and H. L. Cycon, Video coding using a bilinear image warping motion model and wavelet-based residual coding, Proc. SPIE Conf. on Wavelet Applications in Signal and Image Processing, 3813: 401–408, 1999.CrossRefGoogle Scholar
  30. F. Meyer, A. Averbuch, R. Coifman, Multi-layered Image Transcription: Application to a Universal Lossless, submitted.Google Scholar
  31. A. V. Oppenheim, R. W. Shafer, Discrete-time signal processing, Englewood Cliffs, New York, Prentice Hall, 1989.zbMATHGoogle Scholar
  32. A. P. Petukhov, Biorthogonal wavelet bases with rational masks and their applications, Proc. of St. Petersburg Math. Soc., Vol. 7:168 - 193, 1999 (Russian).MathSciNetGoogle Scholar
  33. A. B. Pevnyi and V. A. Zheludev, On the interpolation by discrete splines with equidistant nodes, J. Appr. Th., 102:286–301, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  34. A. Said and W. W. Pearlman, A new, fast and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. on Circ. and Syst. for Video Tech., 6: 243–250, June 1996.CrossRefGoogle Scholar
  35. S. Servetto, K. Ramchandran, M. Orchard, Image Coding Based on a Morphological Representation of Wavelet Data, IEEE Transactions on Image Processing, 8:1161 -1174 Sept. 1999.CrossRefGoogle Scholar
  36. J. Shapiro, Embedded image coding using zerotrees of wavelet coefficients, IEEE Tran. on Signal Processing, 41: 3445–3462, December 1993.zbMATHCrossRefGoogle Scholar
  37. W. Sweldens The lifting scheme: A custom design construction of biorthogonal wavelets, Appl. Comput. Harm. Anal. 3(2):186–200, 1996.MathSciNetzbMATHCrossRefGoogle Scholar
  38. Taubman, D. High Performance Scalable Image Compression with EBCOT, IEEE Tran. on Image Processing, 9:1158 -1170, July 2000.CrossRefGoogle Scholar
  39. Tsai, M. J., Villasenor, J. D., and Chen, F. Stack-Run Image Coding, IEEE Trans. CSVT, 6(5):519–521, Oct. 1996.Google Scholar
  40. M. Unser, A. Aldroubi and M. Eden, A family of polynomial spline wavelet transforms, Signal Processing, 30:141–162, 1993.zbMATHCrossRefGoogle Scholar
  41. S. Saha, and R. Vemuri, Adaptive Wavelet Coding of Multimedia lmages, Proc. ACM Multimedia Conference, Nov. 1999.Google Scholar
  42. G. Strang, and T. Nguen. Wavelets and filter banks, Wellesley-Cambridge Press, 1996.zbMATHGoogle Scholar
  43. V. A. Zheludev, Periodic splines and the fast Fourier transform, Comput. Math. Math. Phys., 32(2):149–165, 1992.MathSciNetzbMATHGoogle Scholar
  44. Xiong, Z., Ramachandran, K. and Orchard, M. T. Space-Frequency Quantization for Wavelet Image Coding, IEEE Trans. IP, vol. 6, no. 5, May 1997, pp. 677–693,Google Scholar
  45. V. A. Zheludev, Wavelet analysis in spaces of slowly growing splines via integral representation, Real Analysis Exchange, 24:229–261, 1998/99.MathSciNetzbMATHGoogle Scholar
  46. W/IEC JTC1/5C29/WG1 N505, Call for contributions for JPEG2000 (ITC 1.29.14, 15444): Image coding system, 1997.Google Scholar
  47. International Organisation for Standardisation (ISO). Call for contributions for JPEG 2000 (JTC 1.29.14, 15444): Image Coding System, March 1997. ISO/IEC JTCl/SC29/WG1 N505.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Amir Z. Averbuch
    • 1
  • Valery A. Zheludev
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

Personalised recommendations