Bayesian wavelet-domain image modeling using hidden Markov trees

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

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

16 Scopus citations

Abstract

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
Title of host publicationIEEE International Conference on Image Processing
Place of PublicationLos Alamitos, CA, United States
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages158-162
Number of pages5
Volume1
StatePublished - Dec 1 1999
EventInternational Conference on Image Processing (ICIP'99) - Kobe, Jpn
Duration: Oct 24 1999Oct 28 1999

Other

OtherInternational Conference on Image Processing (ICIP'99)
CityKobe, Jpn
Period10/24/9910/28/99

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Hardware and Architecture
  • Electrical and Electronic Engineering

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