Skip to main content
Log in

Application Specific Efficient VLSI Architectures for Orthogonal Single- and Multiwavelet Transforms

  • Published:
Journal of VLSI signal processing systems for signal, image and video technology Aims and scope Submit manuscript

Abstract

In this paper, efficient VLSI architectures for orthogonal wavelet transforms with respect to common applications are presented. One class of orthogonal wavelet transforms is the singlewavelet transform which is based on one scaling and one wavelet function. An important application of this transform is signal denoising for which an efficient VLSI implementation and layout is derived in this paper. Contrary to singlewavelets, orthogonal multiwavelets are based on several scaling and wavelet functions. Since they allow properties like compact support, regularity, orthogonality and symmetry, simultaneously, being impossible in the singlewavelet case, multiwavelets are well suited bases for image compression applications. With respect to an efficient implementation of these orthogonal wavelet transforms, approximations of the exact rotation angles of the corresponding wavelet lattice filters are used. The approximations are realized by elementary CORDIC rotations. This method reduces the number of shift and add operations significantly with no influence on the good performance of the transforms. VLSI architectures for the computationally cheap transforms and related implementation aspects are discussed and design examples from architectural level down to layout are given.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. Daubechies, "Ten lectures on wavelets," Notes from the 1990 CBMS-NSF Conference on Wavelets and Applications at Lowell, MA, SIAM, Philadelphia, PA, 1992.

    Google Scholar 

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

    MATH  Google Scholar 

  3. M. Vetterli and C. Herley, "Wavelets and filter banks: Theory and design," IEEE Transactions on Signal Processing, Vol. 40, No. 9, pp. 2207–2232, Sep. 92.

  4. P. Rieder, J. Götze, J.A. Nossek, and C.S. Burrus, "Parameterization of orthogonal wavelet transforms and their simple implementation," IEEE Trans. on Circuits and Systems II, Vol. 45, No. 2, pp. 217–226, Feb. 1998.

    Article  Google Scholar 

  5. P.P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, Englewood Cliffs, NJ, 1992.

    Google Scholar 

  6. P.P. Vaidyanathan and P. Hoang, "Lattice structures for optimal design and robust implementation of two-channel perfectreconstruction QMF banks," IEEE Trans. on ASSP, Vol. 36, No. 1, Jan. 1988.

  7. D.L. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inform. Theory, Vol. 41, pp. 613–627, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Lang and P.N. Heller, "Design of maximally smooth wavelets," Proc. IEEE Int. Conf. Acoust., Speech and Signal Processing, ICASSP 96, Atlanta, Vol. 3, pp. 1463–1466, Mai 1996.

    Google Scholar 

  9. D. Wei, M. Lang, J.E. Odegard, and C.S. Burrus, "Quantization noise reduction using wavelet threshholding for various coding schemes," Proc. SPIE Advanced Algorithms and Architectures for Signal Processing, Vol. 2569, pp. 258–269, July 1995.

    Google Scholar 

  10. U. Simon and M. Berndtgen, Handlich bunt: Kompressionstechniken für Bild-und Videodateien im Vergleich, c't, No. 11, pp. 222–231, Nov. 1996.

  11. J.M. Shapiro, "Embedded image coding using zero-trees of wavelet coefficients," IEEE Transaction on Signal Processing, Vol. 41, No. 12, pp. 3445–3462, Dec. 1993.

    Article  MATH  Google Scholar 

  12. P. Rieder, "Parameterization of symmetric multiwavelets," Proc. IEEE Int. Conf. Acoust., Speech and Signal Processing, ICASSP 97, Munich, Apr. 1997.

  13. P. Rieder and J.A. Nossek, "Smooth multiwavelets based on 2 scaling functions," Proc. IEEE Int. Symp. on Time-Frequency and Time-Scale Analysis, Paris, pp. 309–312, June 1996.

  14. H.S. Malvar and D.H. Staelin, "The LOT: Transform coding without blocking effects," IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. 37, No. 4, pp. 553–559, Apr. 1989.

    Article  Google Scholar 

  15. E.F. Deprettere, G. Hekstra, and R. Heusdens, "Fast VLSI overlapped transform kernel," IEEE Workshop on VLSI Signal Processing, 1995.

  16. J. Götze and G.J. Hekstra, "Adaptive approximate rotations for computing the EVD," in Algorithms and Parallel VLSI Architectures, M. Moonen and F. Cathoor <nt>(Eds.)</nt>, Elsevier Science Publishers, 1994.

  17. B. Haller, J. Götze, and J.R. Cavallaro, "Efficient implementation of rotation operations for high performance QRD-RLS filtering," Proc. IEEE Int. Conf. on Application Specific Systems, Architectures, and Processors, ASAP, pp. 162–174, July 1997.

  18. S. Simon, P. Rieder, C. Schimpfle, and J.A. Nossek, "CORDIC-based architectures for the efficient implementation of discrete wavelet transforms," Proc. IEEE Int. Symp. on Circuits and Systems, ISCAS 96, Atlanta, Vol. IV, pp. 77–80, Mai 1996.

    Google Scholar 

  19. P. Rieder, C.V. Schimpfle, and J.A. Nossek, "Realization of multiwavelet-based transform kernels for image coding," Proc. IEEE Int. Symp. on Circuits and Systems, ISCAS'98, Monterey, 1998.

  20. H. Xie and J.M. Morris, "Design of orthonormal wavelets with better time-frequency resolution," Proc. of SPIE, Wavelet Applications, Orlando, Florida, pp. 878–887, 1994.

  21. S. Trautmann and T.Q. Nguyen, "GenLOT: Design and application for transform-based image coding," Proc. of the Asilomar Conference, Nov. 1995.

  22. C.V. Schimpfle, P. Rieder, and J.A. Nossek, "A power efficient implementation of the discrete cosine transform," Proc. 31st Asilomar Conference on Signals, Systems and Computers, pp. 729–733, 1997.

  23. K.K. Parhi and T. Nishitani, "Folded VLSI architectures for discrete wavelet transform," Proc. IEEE Int. Symp. on Circuits and Systems, ISCAS'93, pp. 1734–1737, 1993.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rieder, P., Simon, S. & Schimpfle, C.V. Application Specific Efficient VLSI Architectures for Orthogonal Single- and Multiwavelet Transforms. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 21, 77–90 (1999). https://doi.org/10.1023/A:1008092020509

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008092020509

Keywords

Navigation