| In this dissertation, we focus on three important topics of image processing based on wavelet transform and Markov random field theory, which are image denoising, image segmentation, and texture synthesis. The main contributions are as follows:We develop a new approach to the wavelet-domain hidden Markov tree model for removing noise from the images. In order to undertake the accuracy of the model parameters and reduce computing expense, we use 3-state hidden Markov tree model(3SHMT) or hierarchical hidden Markov tree model(HHMT) for multiscale statistical image modeling. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of PSNR.A new image segmentation algorithm based wavelet, referred to as joint adaptive context and multiscale segmentation(JACMS) is developed. Towards achieving lower computational complexity, we propose an intelligent parameter initialization and half tree HMT model weighting training algorithm, when applied to image segmentation, this technique provides a reliable initial segmentation. In order to achieve higher accuracies of both texture classification and boundary localization during the interscale fusion, we develop adaptive context structures that are applied to homogeneous regions or/and texture boundaries, respectively. Experiments demonstrate that the proposed algorithms yield excellent segmentation results on both synthetic and real world data examples.A new MRF-based texture synthesis algorithm is proposed. First, the optimal neighbor size is automatically chosen using statistic characteristics similarity between the texture image and its subimage, then the L neighbor matching fast search algorithm is introduced to accelerate texture synthesis. Our texture synthesis methods can produce better results in little time than previous methods.
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