A class of heavy-tailed multivariate non-Gaussian probability models for wavelet coefficients
Fei Shi, Ivan Selesnick · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
It is well documented that the statistical distribution of wavelet coefficients for natural images is non-Gaussian and that neighboring coefficients are highly dependent. In this paper, we propose a new multivariate non-Gaussian probability model to capture the dependencies among neighboring wavelet coefficients in the same scale. The model can be expressed as K exp(-||w||) where w is a N-element vector of wavelet coefficients and ||w|| is a convex combination of l2 norms over subspaces of RN. This model includes the commonly used independent Laplacian model as a special case but it has many more degrees of freedom. Based on this model, the corresponding non-linear threshold (shrinkage) function for denoising is derived using Bayesian estimation theory. Although this function does not have a closed-form solution, a successive substitution method can be used to numerically compute it.