Statistical Image Modeling and Processing Using Wavelet-Domain Hidden Markov Models - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 333

10

Statistical Image Modeling and Processing
Using Wavelet-Domain Hidden
Markov Models

Guoliang Fan and Xiang-Gen Xia

CONTENTS
10.1 Introduction ......................................................... 333

10.2 Wavelet-Domain Hidden Markov Models .......................... 336

....................................................

10.3 Image Denoising 347

10.4 Image Segmentation ................................................. 353

10.5 Texture Analysis and Synthesis ..................................... 366

10.6 Conclusions .......................................................... 382

References .................................................................. 383

10.1 Introduction
In this chapter, we study wavelet-domain hidden Markov models (HMMs)
regarding both statistical image modeling and the application to various im-
age processing problems. As prerequisites, image models often play impor-
tant roles in many image processing applications. Specifically, a statistical
image model regards an image as a realization of a certain probability model,
and predicts a set of possible outcomes weighted by their likelihoods or
probabilities. In this work, we are particularly interested in statistical im-
age modeling and processing using the wavelet-domain HMMs proposed in
Reference 1, where two major mathematical tools are involved, e.g., wavelets
and HMMs.
Wavelets are powerful mathematical tools with flexible multiresolution
structures and many varieties. Although the idea of multiresolution anal-
ysis goes back to the early years of this discipline, it was formally devel-
oped in the 1980s. 2 The construction of compactly supported wavelets 3 has
attracted the attention of the larger scientific community and has stimulated