Skip to main content
EURASIP Journal on Advances in Signal Processing
Download PDF
  • Research Article
  • Open access
  • Published:

Fixed Wordsize Implementation of Lifting Schemes

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 013754 (2006) Cite this article

Abstract

We present a reversible nonlinear discrete wavelet transform with predefined fixed wordsize based on lifting schemes. Restricting the dynamic range of the wavelet domain coefficients due to a fixed wordsize may result in overflow. We show how this overflow has to be handled in order to maintain reversibility of the transform. We also perform an analysis on how large a wordsize of the wavelet coefficients is needed to perform optimal lossless and lossy compressions of images. The scheme is advantageous to well-known integer-to-integer transforms since the wordsize of adders and multipliers can be predefined and does not increase steadily. This also results in significant gains in hardware implementations.

References

  1. Daubechies I, Sweldens W: Factoring wavelet transforms into lifting steps. Journal of Fourier Analysis and Applications 1998,4(3):247-269. 10.1007/BF02476026

    Article  MathSciNet  Google Scholar 

  2. Calderbank AR, Daubechies I, Sweldens W, Yeo B-L: Wavelet transforms that map integers to integers. Applied and Computational Harmonic Analysis 1998,5(3):332-369. 10.1006/acha.1997.0238

    Article  MathSciNet  Google Scholar 

  3. Mertins A, Karp T: Modulated, perfect reconstruction filterbanks with integer coefficients. IEEE Transactions on Signal Processing 2002,50(6):1398-1408. 10.1109/TSP.2002.1003063

    Article  Google Scholar 

  4. Oraintara S, Chen Y-J, Nguyen TQ: Integer fast Fourier transform. IEEE Transactions on Signal Processing 2002,50(3):607-618. 10.1109/78.984749

    Article  MathSciNet  Google Scholar 

  5. Liang J, Tran TD: Fast multiplierless approximations of the DCT with the lifting scheme. IEEE Transactions on Signal Processing 2001,49(12):3032-3044. 10.1109/78.969511

    Article  Google Scholar 

  6. Malvar H, Sullivan G: YCoCg-R: a color space with RGB reversibility and low dynamic range. ISO/IEC JTC1/SC29/WG11 and ITU-T SG16 Q.6, July 2003

    Google Scholar 

  7. Geiger R, Yokotani Y, Schuller G: Improved integer transforms for lossless audio coding. Proceedings of the 37th Asilomar Conference on Signals, Systems and Computers (ACSSC '03), November 2003, Pacific Grove, Calif, USA 2: 2119–2123.

    Google Scholar 

  8. Reichel J, Menegaz G, Nadenau MJ, Kunt M: Integer wavelet transform for embedded lossy to lossless image compression. IEEE Transactions on Image Processing 2001,10(3):383-392. 10.1109/83.908504

    Article  Google Scholar 

  9. Adams MD, Ward RK: Symmetric-extension-compatible reversible integer-to-integer wavelet transforms. IEEE Transactions on Signal Processing 2003,51(10):2624-2636. 10.1109/TSP.2003.816886

    Article  MathSciNet  Google Scholar 

  10. Said A, Pearlman WA: A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Transactions on Circuits and Systems for Video Technology 1996,6(3):243-250. 10.1109/76.499834

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, College of Engineering, Texas Tech University, P.O. Box 43102, Lubbock, TX, 79409-3102, USA

    Tanja Karp

Authors
  1. Tanja Karp
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tanja Karp.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Karp, T. Fixed Wordsize Implementation of Lifting Schemes. EURASIP J. Adv. Signal Process. 2007, 013754 (2006). https://doi.org/10.1155/2007/13754

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/13754

Keywords