Non-Gaussian multivariate probability models and their application to wavelet-based image denoising

This thesis mainly focuses on the development of new probability models for wavelet transform coefficients of natural images. For this purpose, several important statistics of wavelet; coefficients from an image database will be demonstrated. These experiments clearly conclude that the statistics of wavelet coefficients of natural images exhibit non-Gaussian behaviors. One of the characteristics is that the coefficients are uncorrelated, but not independent. Therefore the most common multivariate probability distribution function, multivariate Gaussian, is not suitable for this problem. For this reason, non-Gaussian bivariate and multivariate probability models will be proposed to model the dependencies between coefficients.; One of the contributions of this thesis is the development of new denoising rules taking the dependencies between coefficients into account. Most simple nonlinear thresholding rules for wavelet-based denoising assume the wavelet coefficients are independent and, based on this false assumption, the use of Gaussian and Laplacian probability distribution functions will result in performance degradation. In this thesis, new non-linear shrinkage rules for wavelet based denoising will be derived using Bayesian estimation theory with the proposed non-Gaussian multivariate probability models.; Another contribution of this work is the development of simple but effective data-driven image denoising algorithms. This thesis describes subband and local adaptive image denoising algorithms exploiting interscale and intrascale dependencies using simple newly developed non-linear shrinkage rules which generalize the classical scalar soft thresholding approach. Comparison to effective data-driven techniques in the literature will be given in order to demonstrate the good performance of our algorithms.; The final objective of this thesis is the demonstration that the denoising performance can be improved significantly using redundant wavelet systems. For this purpose, the denoising algorithms will be applied both orthogonal and enhanced wavelet transforms, and performance comparisons will be given.