Bayesian tree-structured image modeling using wavelet-domain hidden Markov models

Justin K. Romberg, Hyeokho Choi, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

439 Scopus citations


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 probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (e.g., using the expectation-maximization algorithm). In this paper, we greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. The simplified model specifies the HMT parameters with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also introduce a Bayesian universal HMT (uHMT) that fixes these nine parameters. The uHMT requires no training of any kind. While extremely simple, we show using a series of image estimation/denoising experiments that these new models retain nearly all of the key image structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both visually and in mean square error.

Original languageEnglish (US)
Pages (from-to)1056-1068
Number of pages13
JournalIEEE Transactions on Image Processing
Issue number7
StatePublished - Jul 2001


  • Hidden Markov tree
  • Statistical image modeling
  • Wavelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition


Dive into the research topics of 'Bayesian tree-structured image modeling using wavelet-domain hidden Markov models'. Together they form a unique fingerprint.

Cite this