Wavelet domain multiresolution Markov models for image segmentation and denoising applications

The advantages of statistical approaches for image modeling and processing are that they can provide a unified view of learning, classification and generation. The wavelet transform, which intends to transform images into a multiresolution representation with both time and frequency characteristics, has already shown its ability as an exciting new tool for multiresolution statistical signal and image processing. In this dissertation, several wavelet domain multiresolution hidden Markov models are studied and proposed in terms of the applications to image denoising and image segmentation. We firstly discuss the wavelet domain Hidden Markov Tree (WHMT) model proposed by Crouse et al., and then we extend this model to unsupervised segmentation because the power of supervised approaches is limited when it is difficult to obtain enough training samples. Several applications of unsupervised segmentation are developed such as texture image segmentation and SAR image segmentation.; To overcome the problem that the segmentation results becomes worse at higher resolution scales by WHMT, we propose a new wavelet domain hierarchical hidden Markov model (HHMM) for multiresolution Bayesian segmentation. The HHMM is constructed based on a hybrid graph structure to represent the distribution properties of wavelet coefficients. A quadtree structure and a pyramidal graph structure are combined together to capture both global and local relationships. The HHMM can obtain both accurate and reliable segmentation results and outperform the WHMT approach.; We also investigate the shift-variance problem caused by real wavelet transforms. A new local hidden Markov model is proposed based on the dual-tree complex wavelet transform that is approximately shift-invariance. Context information is used in this model to indict the local correlation among wavelet coefficients. A new context model based on frequency, orientation and space are introduced to capture both intrascale and interscale dependencies. This algorithm is applied to denoising problems to remove additive white Gaussian noise (AWGN) in an image. Our scheme outruns those approaches based on real wavelet transforms and provides state-of-the-art image denoising performance.