Template Learning using Wavelet Domain Statistical Models

Wavelets have been used with great success in applications such as signal denoising, compression, estimation and feature extraction. This is because of their ability to capture singularities in the signal with a few coefficients. Applications that consider the statistical dependencies of wavelet coefficients have been shown to perform better than those which assume the wavelet coefficients as independent. In this paper, a novel Gaussian mixture model, specifically suited for template learning is proposed for modeling the marginal statistics of the wavelet coefficients. A Bayesian approach for inferring a low dimensional statistical template with a set of training images, using the independent mixture and the hidden Markov tree models extended to the template learning case, is developed. Results obtained for template learning and pattern classification using the low dimensional templates are presented. For training with a large data set, statistical templates generated using the proposed Bayesian approach are more robust than those generated using an information-theoretic framework in the wavelet domain.