Multivariate shrinkage functions for wavelet-based denoising

The first nonlinear rules for wavelet based image denoising assume wavelet coefficients are independent. However it is well known that there are strong dependencies between coefficients such as interscale and intrascale dependencies. We have introduced a non-Gaussian bivariate pdf that exploits the interscale dependencies between a coefficient and its parent. In this paper, how to extend this pdf in order to include the other dependencies will be discussed and in one example, a multivariate shrinkage rule will be derived. The good performance of this new rule will be illustrated on an image denoising algorithm which captures also interscale dependencies.