Bayesian tree-structured image modeling

J. Romberg, Hyeokho Choi, R. G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint statistics of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training (using the EM algorithm, for example). In this paper, we propose two reduced-parameter HMT models that capture the general structure of a broad class of grayscale images. The image HMT (iHMT) model leverages the fact that for a large class of images the structure of the HMT is self-similar across scale. This allows us to reduce the complexity of the iHMT to just nine easily trained parameters (independent of the size of the image and the number of wavelet scales). In the universal HMT (uHMT) we take a Bayesian approach and fix these nine parameters. The uHMT requires no training of any kind. While simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structures modeled by the full HMT. Based on these new models, we develop a shift-invariant wavelet denoising scheme that outperforms all algorithms in the current literature.

Original languageEnglish (US)
Title of host publicationProceedings - 4th IEEE Southwest Symposium on Image Analysis and Interpretation
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)0769505953
StatePublished - 2000
Event4th IEEE Southwest Symposium on Image Analysis and Interpretation, SSIAI 2000 - Austin, United States
Duration: Apr 2 2000Apr 4 2000

Publication series

NameProceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation


Other4th IEEE Southwest Symposium on Image Analysis and Interpretation, SSIAI 2000
Country/TerritoryUnited States


  • Bayesian methods

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computer Science Applications


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