Hierarchical Multiscale Modeling of Wavelet-Based Correlations

  • Zohreh Azimifar
  • Paul Fieguth
  • Ed Jernigan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2396)


This paper presents a multiscale-based analysis of the statistical dependencies between the wavelet coefficients of random fields. In particular, in contrast to common decorrelated-coefficient models, we find that the correlation between wavelet scales can be surprisingly substantial, even across several scales. In this paper we investigate eight possible choices of statistical-interaction models, from trivial models to wavelet-based hierarchical Markov stochastic processes. Finally, the importance of our statistical approach is examined in the context of Bayesian estimation.


Wavelet Transform Wavelet Domain Wavelet Basis Function Hide Markov Tree Hide Markov Tree Model 
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.
    Romberg K., Choi H., and Baraniuk R., ”Bayesian tree-structured image modeling using wavelet-domain hidden markov models,” IEEE trans. an IP, vol. 10, pp. 1056–68, 2001.Google Scholar
  2. 2.
    Portilla J. and Simoncelli E., ”Image denoising via adjustment of wavelet coeflicient magnitude correlation,” Proceedings of the 7th ICIP, Cunudu., 2000.Google Scholar
  3. 3.
    Mumford D. and Huang J., ”Statistics of natural images and models,” Proccedings of International Conference an Computer Vision und Pattern Recognition, 1999.Google Scholar
  4. 4.
    Srivastava A., Liu X., and Grenander U., ”Analytical models for reduced spectral representations of images,” Proceedings of the 8th ICIP, 2001.Google Scholar
  5. 5.
    E. P. Simoncelli, ”Modeling the joint statistics of images in the wavelet domain,” Proceedings of the SPIE 44th Annuul Meeting, 1999.Google Scholar
  6. 6.
    Crouse M. S., Nowak R. D., and Baraniuk R. G., ”Wavelet-based statistical signal processing using hidden markov models,” IEEE trans. an Signal Processing, vol. 46, pp. 886–902, 1998.CrossRefMathSciNetGoogle Scholar
  7. 7.
    Azimifar Z., Fieguth P., and Jemigan E., ”Wavelet shrinkage with correlated wavelet coeflicients,” Proceedings of the 8th ICIP, 2001.Google Scholar
  8. 8.
    Chou K., Willsky A., and Benveniste A., ”Multiscale recuresive estimation, data fusion, and regularization,” IEEE trans. an Automutic Control, vol. 39, pp. 468–478, 1994.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Zohreh Azimifar
    • 1
  • Paul Fieguth
    • 1
  • Ed Jernigan
    • 1
  1. 1.Department of Systems Design EngineeringUniversity of WaterlooWaterlooCanada

Personalised recommendations