Skip to main content
SpringerLink
Log in

Coarse-Grained Parallel Algorithms for Multi-Dimensional Wavelet Transforms

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

This paper presents parallel algorithms for computing multi-dimensional wavelet transforms on both shared memory and distributed memory machines. Traditional data partitioning methods for n-dimensional Discrete Wavelet Transforms (DWTs) call for data redistribution once a one dimensional wavelet transform is computed along each dimension. To avoid the data communication inherent in this redistribution, two new partitioning methods called CRBP (Communication Reduced Block Partitioning) and CRLP (Communication Reduced Layer Partitioning) are proposed. The efficiency of the algorithms is compared through several examples implemented on a cluster of SGI workstations. Two kinds of parallel approaches are used to compute multi-dimensional wavelet transforms on shared memory machines: homogeneous parallelism, and heterogeneous parallelism. Homogeneous parallelism uses traditional data partitioning while heterogeneous parallelism uses the CRBP approach. The effectiveness of these approaches is demonstrated through several examples implemented on an SGI Power Challenge. The paper discusses the effectiveness of each of the approaches on the two kinds of architectures.

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

Access this article

Log in via an institution

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. Caulfield, H. J. 1992. Parallel discrete and continuous wavelet transforms. Optical Engineering, 31, 1835–1839.

    Google Scholar 

  2. Daubechies, I. 1992. Ten Lectures on Wavelets. Philadelphia: SIAM.

    Google Scholar 

  3. Foster, I. T. 1994. Designing and building parallel programs. New York: Addison-Wesley Publishing Company.

    Google Scholar 

  4. Gropp, W., Lusk, E., & Skjellum, A. 1996. A high-performance, portable implementation of the MPI message passing interface standard.

  5. Holmström, Mats. 1995. Parallelizing the fast wavelet transform. Parallel Computing, 21, 1837–1848.

    Google Scholar 

  6. Hoyt, J. D., & Weschsler, H. 1992. The Wavelet Transform-a CMOS VLSI ASIC implementation. Pages 19–22 of: 11th IAPR International Conference on Pattern Recongnition, vol. IV.

  7. Kita, Takuro. 1993. The optimum approximation of multi-dimensional signals using parallel wavelet filter banks. IEICE Trans. Fundamentals, E76-A, 1830–1848.

    Google Scholar 

  8. Lega, E., Scholl, H., Alimi, J. M., Bijaoui, A., & Bury, P. 1995. A Parallel algorithm for structure detection based on Wavelet and segmentation analysis. Parallel Computing, 21, 265–285.

    Google Scholar 

  9. Lu, J. 1993. Parallelizing Mallat Algorithm for 2-d Wavelet Transform. Information Processing Letters, 45, 255–259.

    Google Scholar 

  10. Misra, M., & Nichols, T. 1994. Computation of 2-D wavelet transforms on the Connection Machine-2. Pages 1–10 of: Proceedings of the International Conference on Applications in Parallel and Distributed Computing.

  11. Misra, M., & Prasanna, V. K. 1992. Parallel computation of wavelet transforms. In: Proceeding of the 11th International Conference on Pattern Recognition.

  12. Pacheco, Peter S. 1997. Parallel Programming with MPI. San Francisco, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  13. Parhi, K. K., & Nishitani, T. 1993. VLSI arichitectures for discrete wavelet transforms. IEEE Transactions on Very Large Scale Integration Systems, 1, 191–202.

    Google Scholar 

  14. Pic, M. M., & Essafi, H. 1993. Wavelet Transform on Connection Machine and Sympatia. Int. J. Modern Physics, 4, 97–103.

    Google Scholar 

  15. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992. Numerical Recipes in C. New York: Cambridge University Press.

    Google Scholar 

  16. Sahinoglou, H., & Cabrera, S. D. 1991. A high-speed pyramid image coding algorithm for a VLSI implementation. IEEE Transactions on Circuits and Systems, 1, 369–374.

    Google Scholar 

  17. Strang, G., & Nguyen, T. 1996. Wavelets and Filter Banks. Wellesley: Cambridge Press.

    Google Scholar 

  18. Wickerhauser, M. V. 1992. Acoustic signal compression with wavelet packets. Wavelet Analysis and Its Applications, Chui, C. K. (ed.), 679–700.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO, 80401

    Linda Yang & Manavendra Misra

Authors
  1. Linda Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manavendra Misra
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, L., Misra, M. Coarse-Grained Parallel Algorithms for Multi-Dimensional Wavelet Transforms. The Journal of Supercomputing 12, 99–118 (1998). https://doi.org/10.1023/A:1007985629329

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007985629329

Search

Navigation