Hidden Markov tree model of images using quaternion wavelet transform

The quaternion wavelet transform is regarded as a new multi-scale tool for signal and image processing, which can effectively capture local shifts and image texture information. The marginal and joint distributions of the quaternion wavelet transform coefficients are measured by the histogram. The mutual information is utilized to measure the dependence between the coefficients. The authors have drawn the conclusion that the quaternion coefficients can be modeled by a Gaussian Mixture model conditioned to the magnitudes of generalized coefficients, with intensive analysis of the statistical properties of the decomposition coefficients. In this paper a new hidden Markov tree model utilizing quaternion wavelet transforms is proposed based on the authors' findings. In order to demonstrate its effectiveness, the new statistical model was applied to image de-noising. The experimental results show that the proposed statistical model exhibits better performance than other related image de-noising algorithms that are also based on hidden Markov tree models. (C) 2014 Elsevier Ltd. All rights reserved.