Skip to main content

Two-Dimensional Wavelet Transforms and Applications

  • Chapter
Book cover Wavelets and Subbands

Abstract

In this chapter, we describe various methods of applying the wavelet transform to a two-dimensional signal or image. In particular, we will treat subband image decomposition and encoding, image enhancement, and wavelet techniques for image compression and video encoding. Optical image processing techniques using wavelets will be the subject of a later chapter.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Abbate, J. Frankel, and P. Das, Application of wavelet image processing for ultrasonic gaging, Proc. 1997 SPIE Conference on Wavelets, 1997.

    Google Scholar 

  2. E. H. Adelson, E. Simoncelli, and R. Hingomni, Orthogonal pyramid transforms for image coding, Proc. SPIE, vol. 845, pp. 50–58, 1987.

    Article  Google Scholar 

  3. R. Ansari, H. Gaggioni, and D. J. LeGall, HDTV coding using a nonrectangular subband decomposition, Proc. SPIE Conf. Visual Commun. Image Processing, pp. 821–824, 1988.

    Google Scholar 

  4. T. C. Bell, J. G. Cleary, and I. H. Witten, Text Compression, Prentice-Hall, Englewood Cliffs, NJ, 1990.

    Google Scholar 

  5. P.J. Burt and E.H. Andelson, The Laplacian pyramid as a compact image code, IEEE Trans. Commun., vol. 31, pp. 532–540, 1983.

    Article  Google Scholar 

  6. W. Chen, and W. Pratt, Scene adaptive coder, IEEE Trans. Comm., vol. COM-32, pp. 225–232, 1984.

    Article  Google Scholar 

  7. R.R. Coifman and M. V. Wickerhauser, Entropy-based algorithms for best basis selection, IEEE Trans. Inform. Theory, vol. 38, pp. 713–718, 1992.

    Article  MATH  Google Scholar 

  8. J.G. Daugman, Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters, J. Opt. Soc. Am., vol. A2, 1160–1169, 1985.

    Article  Google Scholar 

  9. I. Daubechies, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math, vol. XLI, pp. 909–996, 1988.

    Article  MathSciNet  Google Scholar 

  10. R. A. DeVore, B. Lawerth, and B. J. Lucier, Image compression through wavelet transform coding, IEEE Trans. Inform. Theory, vol. 38, pp. 719–746, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Effros. P. A. Chou. E. A. Riskin. and R. M. Gray, A progressive universal noiseless coder, IEEE Trans. Inform. Theory, vol, 40, pp. 108–117, 1994.

    Article  MATH  Google Scholar 

  12. W. Equitz and T. Cover, Successive refinement of information, IEEE Trans. Inform. Theory, vol. 37, pp. 269–275, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Estaban and C. Galand, Application of quadrature mirror filters to split band voice coding schemes, Proc. ICASSP, pp. 191–195, 1977.

    Google Scholar 

  14. D. Gabor, Theory of communication, J. Inst. Elec. Eng., vol. 93, pp. 429–457, 1946.

    Google Scholar 

  15. H. Gharavi and A. Tabatabai, Application of quadrature mirror filtering to the coding of monochrome and color images, Proc. ICASSP, pp. 2384–2387, 1987.

    Google Scholar 

  16. V. K. Heer and H.-E. Reinfelder, A comparison of reversible methods for data compression, Proc. SPIE, vol. 1233, pp. 354–365, 1990.

    Article  Google Scholar 

  17. Y. Huang, H. M. Driezen, and N. P. Galatsanos, Prioritized DCT for Compression and Progressive Transmission of Images, IEEE Trans. Image Process., vol. 1, pp. 477–487, 1992.

    Article  Google Scholar 

  18. N. S. Jayant and P. Noll, Digital Coding of Waveforms, Prentice-Hall, Englewood Cliffs, NJ, 1984

    Google Scholar 

  19. Y. H. Kim and L. W. Modestino, Adaptive entropy coded subband coding of images, IEEE Trans. Image Process., vol. 1. pp. 31–48. Jan. 1992.

    Article  Google Scholar 

  20. G. R. Kuduvalli and R. M. Rangayyan, Performance analysis of reversible image compression techniques for high-resolution digital teleradiology, IEEE Trans. Med Imaging, vol.MI-1, pp. 430–445, 1992.

    Article  Google Scholar 

  21. A. S. Lewis and O. Knowles, A 64 kB/s video Codec using the 2-D wavelet transform, in Proc. Data Compression Conf, Snowbird, Utah, IEEE Computer Society Press, 1991

    Google Scholar 

  22. A.S. Lewis and O. Knowles, Image compression using the 2-D wavelet transform, IEEE Trans. Image Process., vol. 1, pp. 244–250, 1992.

    Article  Google Scholar 

  23. S. G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans, on Pattern Analys. and Machine IntelL, vol. 11m n. 7, pp. 674–693, 1989.

    Article  Google Scholar 

  24. S. Mallat, Multifrequency channel decompositions of images and wavelet models, IEEE Trans. Acoiist. Speech Signal Process., vol. 37, pp. 2091–2110, 1990.

    Article  Google Scholar 

  25. A Pentland and B. Horowitz, A practical approach to fractal-based image compression, Proc. Data Compression Conf., Snowbird, Utah, 1991.

    Google Scholar 

  26. W. H. Press. B. P Flannery, S. A. Teukolsky. and W. T. Vetterling. Numerical Recipes: The Art of Scientific Programming, University Press, Cambridge, 1986.

    Google Scholar 

  27. M. Rabbani and P. W. Jones, Digital Image Compression Techniques, SPIE, Bellingham, WA, 1991.

    Book  Google Scholar 

  28. M. Rabbani and P. W. Melnychuck., Conditioning contexts for the arithmetic coding of bit planes, IEEE Trans. Signal Process., vol. 40, pp. 232–236. Jan. 1992.

    Article  Google Scholar 

  29. S. Ranganath and H. Blume, Hierarchical image decomposition and filtering using the S-transform,. in Proc. SPIE, vol. 914. pp. 799–814, 1988.

    Article  Google Scholar 

  30. O. Rioul and M. Vetterli, Wavelets and signal processing, IEEE Signal Proc. Mag., pp. 14–38, 1991.

    Google Scholar 

  31. P. Roos, A. Viergever, and M. C. A. van Dijke, Reversible intraframe compression of medical images, IEEE Trans. Med. Imaging, vol. 7. pp. 328–336, Sept. 1988.

    Article  Google Scholar 

  32. A. Said and W. A. Pearlman, Reversible image compression via multiresolution representation and predictive coding, in Proc. SPIE, vol. 2094. pp. 664–674, 1993.

    Article  Google Scholar 

  33. A. Said and W. A. Pearlman, A new fast and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Tech., vol. 6. pp. 243–250, June 1996.

    Article  Google Scholar 

  34. A. Said and W. Pearlman, An image multiresolution representation for lossless and lossy compression, IEEE Trans. Image Process., vol. 5, pp. 1303–1309, 1996.

    Article  Google Scholar 

  35. A. Said and W. Pearlman, A new, fast, and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits and Syst. Video Tech., Vol. 6, p. 243–249, 1996.

    Article  Google Scholar 

  36. K. Sayood and K. Anderson, A differential lossless image compression scheme, IEEE Trans. Signal Process., vol. 40. pp. 236–241, 1992.

    Article  Google Scholar 

  37. J. M. Shapiro, An embedded wavelet hierarchical image coder, Proc. IEEE Int. Conf. Acoiist., Speech, Signal Processing, 1992.

    Google Scholar 

  38. J. M. Shapiro, Embedded image coding using zerotrees of wavelets coefficients, IEEE Trans. Signal Processing, vol. 41. pp. 3445–3462, Dec. 1993.

    Article  MATH  Google Scholar 

  39. S. Takamura and M. Takagi, Lossless image compression with lossy image using adaptive prediction and arithmetic coding, Proc.of the Conference on Data Compression, pp. 166–174, 1994.

    Google Scholar 

  40. S. Todd, G. G. Langdon Jr., and J. Rissanen, Parameter reduction and context selection for compression of grey-scale images, IBM J. Res. Dew, vol. 29, pp. 188–193, 1985.

    Article  Google Scholar 

  41. A.K. Tran, K. Liu, Tzou and E. Vogel, An efficient pyramid image coding scheme, Proc. ICASSP, pp. 744–747, 1987.

    Google Scholar 

  42. J. Vaisey and A. Gersho, Image compression with variable block size segmentation, IEEE Trans. Signal Process., vol. 2040, Aug. 1992.

    Google Scholar 

  43. M. Vetterli, J. Kovacevic, and D. J. LeGall, Perfect reconstruction filter banks for HDTV representation and coding, Image Commun., vol. 2, pp. 349–364, Oct. 1990.

    Google Scholar 

  44. G. K. Wallace, The JPEG still picture compression standard, Comm. ACM. vol. 34, pp. 30–44, Apr. 1991.

    Article  Google Scholar 

  45. G.G. Walter, A sampling theorem for wavelet subspaces, IEEE Trans. Inform. Theory, vol. 38, pp. 881–884, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  46. H. Witten, R. Neal, and J. G. Cleary, Arithmetic coding for data compression, Comm. ACM, vol. 30, pp. 520–540, June 1987.

    Article  Google Scholar 

  47. G. W. Womell, A Karhunen-Louve expansion for 1/f processes via wavelets, IEEE Trans. Inform. Theory, vol. 36, pp. 859–861, 1990.

    Article  Google Scholar 

  48. J. W. Woods ed., Subband Image Coding, Kluwer, Boston, 1991.

    MATH  Google Scholar 

  49. Z. Xiong, N. Galatsanos, and M. Orchard, Marginal analysis prioritization for image compression based on a hierarchical wavelet de-composition, in Proc. IEEE Int. Conf Acoust., Speech, Signal Processing, 1993.

    Google Scholar 

  50. W. Zettler, I. Huffman, and D. C. P. Linden, Applications of compactly supported wavelets to image compression, SPIE Image Processing Algorithms, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Abbate, A., DeCusatis, C.M., Das, P.K. (2002). Two-Dimensional Wavelet Transforms and Applications. In: Wavelets and Subbands. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0113-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0113-7_6

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6618-1

  • Online ISBN: 978-1-4612-0113-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics