From Lossy to Lossless Wavelet Image Coding in a Tree-Based Encoder with Resolution Scalability

  • Jose Oliver
  • Manuel P. Malumbres
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4225)


For a lossy encoder, it is important to be able to provide also lossless compression with little or no modification of the usual algorithm, so that an implementation of that algorithm can work in lossy or lossless mode, depending on the specific application, simply by varying the input parameters. In this paper, we evaluate the capability of the Lower Tree Wavelet (LTW) image encoder to work in lossless mode. LTW is a fast and multiresolution wavelet image encoder, which uses trees as a fast mode to group coefficients. In addition, general details on how to implement efficiently (i.e., with only shift and addition/subtraction operations) a reversible integer-to-integer wavelet transform are also given, as a requirement to implement a wavelet-based lossless encoder. Numerical results show that despite being general purpose (i.e., both lossy and lossless) and lacking of complex techniques (such as high-order context and predictive coding), the LTW performs as well as JPEG 2000 in lossless mode, and only 5% below LOCO-I, a specific lossless algorithm.


Wavelet Coefficient Image Encoder Predictive Code Lossless Compression Lift Scheme 
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.


  1. 1.
    Wu, X., Memon, N.D.: CALIC- A Context Based Adaptive Lossless Image Coding Scheme. IEEE Transactions on Communications 45, 437–444 (1996)CrossRefGoogle Scholar
  2. 2.
    Weinberger, M., Seroussi, G., Sapiro, G.: The LOCO-I Lossless Image Compression Algorithm: Principles and Standardization into JPEG-LS. IEEE Transactions on Image Processing 9, 1309–1324 (2000)CrossRefGoogle Scholar
  3. 3.
    ISO/IEC 15444-1: JPEG2000 image coding system (2000)Google Scholar
  4. 4.
    Said, A., Pearlman, A.: A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Transactions on circuits and systems for video technology 6(3) (June 1996)Google Scholar
  5. 5.
    Shapiro, J.M.: Embedded image coding using zerotrees of wavelet coefficients. IEEE Transactions on Signal Processing 41(12) (December 1993)Google Scholar
  6. 6.
    Oliver, J., Malumbres, M.P.: Fast and Efficient Spatial Scalable Image Compression Using Wavelet Lower Trees. In: Proc. IEEE Data Compression Conference, Snowbird, UT (March 2003)Google Scholar
  7. 7.
    Mallat, S.: A Theory for Multiresolution Signal Decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 674–693 (1989)MATHCrossRefGoogle Scholar
  8. 8.
    Sweldens, W.: The lifting scheme: a custom-design construction of biorthogonal wavelets. Journal of Applied Computational and Harmonic Analysis 3, 186–200 (1996)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Calderbank, R.C., Daubechies, I., Sweldens, W., Yeo, B.L.: Wavelet transforms that map integers to integer. Journal of Applied Computational and Harmonic Analysis 5, 332–369 (1998)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Adams, M., Kossentini, F.: Reversible Integer-to-Integer Wavelet Transforms for Image Compression: Performance Evaluation and Analysis. IEEE Transactions on Image Processing 9, 1010–1024 (2000)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Antonini, M., Barlaud, M., Mathieu, P., Daubechies, I.: Imagen Coding Using Wavelet Transform. IEEE Transactions on Image Processing 1(2) (April 1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jose Oliver
    • 1
  • Manuel P. Malumbres
    • 2
  1. 1.Department of Computer Engineering (DISCA)Technical University of ValenciaValenciaSpain
  2. 2.Departamento de física y ATCMiguel Hernández UniversityElcheSpain

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