A class of multivariate non-Gaussian probability models and the application to wavelet-based image processing

This thesis mainly focuses on the development of a class of new non-Gaussian probability models for wavelet coefficients of natural images and the corresponding Bayesian denoising algorithm. A multivariate quasi-Laplacian model is first introduced as a generalization of the single-variable Laplacian distribution to multi-dimensions. A mixture of this model is used as the wavelet coefficient prior for Bayesian wavelet-based image denoising. The mixture model well fits the marginal distribution of wavelet coefficients. Although a stationary probability model, it is able to capture the dependencies among a group of coefficients. The weak but non-negligible correlations between coefficients can also be modeled. The Expectation-Maximization algorithm is used for estimating the model parameters from the observed noisy data. Efficient approximations of the Bayesian MMSE estimates for denoising are found.; Various model options are tested through experiments and the best combination is discovered. The denoising algorithm is applied on both separable wavelet transform and directional representations of images such as the dual-tree complex wavelet transform and the steerable pyramid. The non-white Gaussian noise associated with non-orthogonal transforms is allowed in the Bayesian estimation scheme developed. The performance of the proposed algorithm is compared with existing techniques in both PSNR values and visual qualities. Our results are comparable to or better than state-of-the-art techniques in both aspects.; A similar mixture model is also used for wavelet-based image enhancement tasks, where a non-linear mapping function is derived and satisfactory enhancement results are obtained.