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A Parallel Architecture for the 2-D Discrete Wavelet Transform with Integer Lifting Scheme

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Abstract

In this paper we propose a dedicated architecture to implement a 2-D discrete wavelet transform computed by adopting the new lifting scheme framework. Through this new construction tool it is possible to obtain integer versions of the wavelet transform. This is a very interesting issue when the goal is lossless compression of images, whose pixels are represented through integers. In the classical approach to the discrete wavelet, the filter coefficients are real numbers and so are the resulting coefficients. When pursuing hardware implementations for real time and embedded applications, this causes the need to manage fixed point operations and unavoidable quantization. If the output can be produced with integer values instead, perfect reconstruction and lossless compression are possible. Typical applications include scenarios with limited bandwidth and big image sizes, such as medical imaging for tele-medicine or satellite image transmission, not suited to lossy compression, or high quality images in digital cameras.

We analyze the data flow and dependencies to define an architecture to implement the integer lifting wavelet transform. The paper covers all lifting implementations based on a single ‘lifting stepr’ and uses the Deslauriers-Dubuc (4, 2) filter as a guiding example, but the approach is general and the results can be easily extended to other filters. We outline a very general framework, to be used either in a custom VLSI implementation, or in mappings onto existing ‘computing cells’. The overall resources needed are less than those for the equivalent classical FIR version computed through a systolic architecture.

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References

  1. S. Mallat, "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Trans. on Pattern Analysis and Machine Intell., vol. 11, no. 7, 1989, pp. 674–693.

    Article  MATH  Google Scholar 

  2. O. Rioul and M. Vetterli, "Wavelets and Signal Processing," IEEE Signal Processing Magazine, Oct. 1991, pp. 14–37.

  3. G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, MA, 1996.

    MATH  Google Scholar 

  4. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Englewood Cliffs, NJ: Prentice-Hall 1995.

    MATH  Google Scholar 

  5. M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, "Im-ages Coding Using Wavelet Transform," IEEE Trans. Image Pro-cessing, vol. 1, no. 2, 1992, pp. 205–220.

    Article  Google Scholar 

  6. A. Said and W.A. Pearlman, "A New Fast and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees," IEEE Trans. on Circuits and Systems for Video Technology, vol. 6, no. 3, 1996, pp. 243–250.

    Article  Google Scholar 

  7. J.M. Shapiro, "Embedded Image Coding Using Zerotrees of Wavelet Coefficients," IEEE Trans. Signal Processing, vol. 41, 1993, pp. 3445–3462.

    Article  MATH  Google Scholar 

  8. H.Y.H. Chuang and L. Chen, "VLSI Architectures for Fast 2D Discrete Orthonormal Wavelet Transform," Journal of VLSI Signal Processing, vol. 10, 1995, pp. 225–236.

    Article  Google Scholar 

  9. C. Chakrabarthi and M. Vishwanath, "Efficient Realizations of the Discrete and Continuous Wavelet Transform: From Single Chip Implementations to Mappings on Simd Array Computers," IEEE Trans. on Signal Processing, vol 43, no. 3, 1995, pp. 759–771.

    Article  Google Scholar 

  10. J. Fridman and E.S. Manolakos, "Discrete Wavelet Transform: Data Dependence Analysis and Synthesis of Distributed Memory and Control Array Architectures," IEEE Transaction on Signal Processing, vol. 45, no. 5, 1997, pp. 1291–1308.

    Article  Google Scholar 

  11. R. Lang, E. Plesner, H. Schroder, and A. Spray, "An Efficient Systolic Architecture for the One-dimensional Wavelet Transform," SPIE, vol. 2242, (Wavelet Applications), 1994, pp. 925–935.

    Article  Google Scholar 

  12. M. Vishwanath, R.M. Owens, and M.J. Irwin, "VLSI Archi-tectures for the Discrete Wavelet Transform," IEEE Trans. on Circuits and Systems-II: Analog and Digital Signal Processing, vol. 42, no. 5, 1995, pp. 305–316.

    Article  MATH  Google Scholar 

  13. G. Seaman, "A Latency-Hiding MIMD Wavelet Transform," in Proceedings of the 4th Euromicro Workshop on Parallel and Distributed Processing, Praga, Jan., 1996, pp. 22–26.

  14. K.K. Parhi and T. Nishitani, "VLSI Architectures for Discrete Wavelet Transforms," IEEE Trans. on Very Large Scale Integration, vol. 1, no. 2, 1993, pp. 191–202.

    Article  Google Scholar 

  15. M. Misra and T. Nichols, "Computation of 2-D Wavelet Trans-forms on the Connection Machine-2," Itip Transactions A, vol. 44, 1994, pp. 3–12.

    Google Scholar 

  16. M. Ferretti and D. Rizzo, "Wavelet Transform Architectures: A System Level Review," in International Conference on Image Analysis and Processing, ICIAP'97, Florence, 17–19 September 1997, vol. II, pp. 77–84.

    Google Scholar 

  17. W. Sweldens," The Lifting Scheme: A Custom-Design Con-struction of Biorthogonal Wavelets," Applied and Computa-tional Harmonic Analysis (ACHA), vol. 3, no. 2, 1996, pp. 186–200.

    Article  MathSciNet  MATH  Google Scholar 

  18. W. Sweldens, "The Lifting Scheme: A Construction of Second Generation Wavelets," SIAM J. Math. Anal., vol. 29, no. 2, 1997, pp. 511–546.

    Article  MathSciNet  Google Scholar 

  19. S.K. Rao and T. Kailath, "Architecutre Design for Regular It-erative Algorithms," in Systems and Signal Processing Systems, E.E. Schwartzlander Jr., Ed., New York, NY: Marcel Dekker, 1987, pp. 209–257.

    Google Scholar 

  20. M. Vishwanath, "The Recursive Pyramid Algorithm for the Dis-crete Wavelet Transform," IEEE Trans. on Signal Processing, vol. 42, no. 3, 1994, pp. 673–677.

    Article  Google Scholar 

  21. M. Ferretti and D. Rizzo, "Handling Borders in Systolic Ar-chitectures for the 1-D Discrete Wavelet Transform for Perfect Reconstruction," IEEE Signal Processing, vol. 48, no. 5, 2000, pp. 1365–1378.

    Article  Google Scholar 

  22. I. Daubechies and W. Sweldens, "Factoring Wavelet Transform into Lifting Steps," J. Fourier Anal. Appl., vol. 4, no. 3, 1998, pp. 247–269.

    Article  MathSciNet  MATH  Google Scholar 

  23. A.R. Calderbank, I. Daubechies, W. Sweldens, and B.L. Yeo, "Wavelet Transform that Map Integers to Integers," Applied and Computational Harmonic Analysis (ACHA), vol. 5, no. 3, 1998, pp. 332–369.

    Article  MathSciNet  MATH  Google Scholar 

  24. G. Lafruit, L. Nachtergaele, J. Bormans, M. Engels, and I. Bolsen, "Optimal Memory Organization for Scalable Texture Codecs in MPEG-4," IEEE Trans. on Circuits and Systems for Video Technology, vol. 9, no. 2, 1999, pp. 218–243.

    Article  Google Scholar 

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  1. DIS, University of Pavia, Via Ferrata 1, 27100, Pavia, Italy

    M. Ferretti & D. Rizzo

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  1. M. Ferretti
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  2. D. Rizzo
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Ferretti, M., Rizzo, D. A Parallel Architecture for the 2-D Discrete Wavelet Transform with Integer Lifting Scheme. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 28, 165–185 (2001). https://doi.org/10.1023/A:1011161423836

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